Subjects -> MATHEMATICS (Total: 1013 journals)
    - APPLIED MATHEMATICS (92 journals)
    - GEOMETRY AND TOPOLOGY (23 journals)
    - MATHEMATICS (714 journals)
    - MATHEMATICS (GENERAL) (45 journals)
    - NUMERICAL ANALYSIS (26 journals)
    - PROBABILITIES AND MATH STATISTICS (113 journals)

MATHEMATICS (714 journals)                  1 2 3 4 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 3)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 2)
Accounting Perspectives     Full-text available via subscription   (Followers: 4)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 13)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 5)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Hybrid Journal   (Followers: 41)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 2)
Acta Mathematica Hungarica     Hybrid Journal   (Followers: 3)
Acta Mathematica Sinica, English Series     Hybrid Journal   (Followers: 5)
Acta Mathematica Vietnamica     Hybrid Journal  
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal  
Advanced Science Letters     Full-text available via subscription   (Followers: 9)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 5)
Advances in Catalysis     Full-text available via subscription   (Followers: 7)
Advances in Complex Systems     Hybrid Journal   (Followers: 10)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 20)
Advances in Decision Sciences     Open Access   (Followers: 4)
Advances in Difference Equations     Open Access   (Followers: 2)
Advances in Fixed Point Theory     Open Access  
Advances in Geosciences (ADGEO)     Open Access   (Followers: 19)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 9)
Advances in Materials Science     Open Access   (Followers: 20)
Advances in Mathematical Physics     Open Access   (Followers: 6)
Advances in Mathematics     Full-text available via subscription   (Followers: 21)
Advances in Numerical Analysis     Open Access   (Followers: 4)
Advances in Operations Research     Open Access   (Followers: 13)
Advances in Operator Theory     Hybrid Journal  
Advances in Pure Mathematics     Open Access   (Followers: 9)
Advances in Science and Research (ASR)     Open Access   (Followers: 8)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2)
African Journal of Educational Studies in Mathematics and Sciences     Full-text available via subscription   (Followers: 7)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 5)
Afrika Matematika     Hybrid Journal   (Followers: 2)
Air, Soil & Water Research     Open Access   (Followers: 6)
AKSIOMATIK : Jurnal Penelitian Pendidikan dan Pembelajaran Matematika     Open Access  
Al-Jabar : Jurnal Pendidikan Matematika     Open Access  
Al-Qadisiyah Journal for Computer Science and Mathematics     Open Access   (Followers: 2)
AL-Rafidain Journal of Computer Sciences and Mathematics     Open Access   (Followers: 3)
Algebra and Logic     Hybrid Journal   (Followers: 7)
Algebra Colloquium     Hybrid Journal   (Followers: 1)
Algebra Universalis     Hybrid Journal   (Followers: 2)
Algorithmic Operations Research     Open Access   (Followers: 5)
Algorithms     Open Access   (Followers: 13)
Algorithms Research     Open Access   (Followers: 1)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 8)
American Journal of Mathematical Analysis     Open Access   (Followers: 1)
American Journal of Mathematical and Management Sciences     Hybrid Journal  
American Journal of Mathematics     Full-text available via subscription   (Followers: 8)
American Journal of Operations Research     Open Access   (Followers: 6)
American Mathematical Monthly     Full-text available via subscription   (Followers: 3)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 12)
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access  
Analysis and Applications     Hybrid Journal   (Followers: 2)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 9)
Anargya : Jurnal Ilmiah Pendidikan Matematika     Open Access  
Annales Mathematicae Silesianae     Open Access  
Annales mathématiques du Québec     Hybrid Journal   (Followers: 3)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica     Open Access   (Followers: 1)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica     Open Access  
Annali di Matematica Pura ed Applicata     Hybrid Journal   (Followers: 1)
Annals of Combinatorics     Hybrid Journal   (Followers: 3)
Annals of Data Science     Hybrid Journal   (Followers: 14)
Annals of Functional Analysis     Hybrid Journal   (Followers: 2)
Annals of Mathematics     Full-text available via subscription   (Followers: 5)
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 16)
Annals of PDE     Hybrid Journal  
Annals of Pure and Applied Logic     Open Access   (Followers: 4)
Annals of the Alexandru Ioan Cuza University - Mathematics     Open Access   (Followers: 1)
Annals of the Institute of Statistical Mathematics     Hybrid Journal   (Followers: 1)
Annals of West University of Timisoara - Mathematics     Open Access   (Followers: 1)
Annuaire du Collège de France     Open Access   (Followers: 6)
ANZIAM Journal     Open Access   (Followers: 1)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 3)
Applications of Mathematics     Hybrid Journal   (Followers: 2)
Applied Categorical Structures     Hybrid Journal   (Followers: 4)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 16)
Applied Mathematics     Open Access   (Followers: 7)
Applied Mathematics     Open Access   (Followers: 6)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 11)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal   (Followers: 1)
Applied Mathematics and Nonlinear Sciences     Open Access  
Applied Mathematics Letters     Full-text available via subscription   (Followers: 1)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 1)
Applied Network Science     Open Access   (Followers: 3)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 4)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 5)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 3)
Arabian Journal of Mathematics     Open Access   (Followers: 1)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 3)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 4)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 5)
Armenian Journal of Mathematics     Open Access  
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites     Open Access   (Followers: 22)
Asia-Pacific Journal of Operational Research     Hybrid Journal   (Followers: 3)
Asian Journal of Algebra     Open Access   (Followers: 1)
Asian Research Journal of Mathematics     Open Access  
Asian-European Journal of Mathematics     Hybrid Journal   (Followers: 2)
Australian Mathematics Teacher, The     Full-text available via subscription   (Followers: 7)
Australian Primary Mathematics Classroom     Full-text available via subscription   (Followers: 4)
Australian Senior Mathematics Journal     Full-text available via subscription   (Followers: 1)
Automatic Documentation and Mathematical Linguistics     Hybrid Journal   (Followers: 5)
Axioms     Open Access   (Followers: 1)
Baltic International Yearbook of Cognition, Logic and Communication     Open Access   (Followers: 2)
Banach Journal of Mathematical Analysis     Hybrid Journal  
Basin Research     Hybrid Journal   (Followers: 7)
BIBECHANA     Open Access  
Biomath     Open Access  
BIT Numerical Mathematics     Hybrid Journal  
Boletim Cearense de Educação e História da Matemática     Open Access  
Boletín de la Sociedad Matemática Mexicana     Hybrid Journal  
Bollettino dell'Unione Matematica Italiana     Full-text available via subscription  
British Journal for the History of Mathematics     Hybrid Journal   (Followers: 2)
British Journal of Mathematical and Statistical Psychology     Full-text available via subscription   (Followers: 18)
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 1)
Bulletin des Sciences Mathamatiques     Full-text available via subscription   (Followers: 3)
Bulletin of Dnipropetrovsk University. Series : Communications in Mathematical Modeling and Differential Equations Theory     Open Access   (Followers: 2)
Bulletin of Mathematical Sciences     Open Access   (Followers: 1)
Bulletin of Symbolic Logic     Full-text available via subscription   (Followers: 4)
Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics     Open Access  
Bulletin of the Australian Mathematical Society     Full-text available via subscription   (Followers: 2)
Bulletin of the Brazilian Mathematical Society, New Series     Hybrid Journal  
Bulletin of the Iranian Mathematical Society     Hybrid Journal  
Bulletin of the London Mathematical Society     Hybrid Journal   (Followers: 3)
Bulletin of the Malaysian Mathematical Sciences Society     Hybrid Journal  
Cadernos do IME : Série Matemática     Open Access  
Calculus of Variations and Partial Differential Equations     Hybrid Journal  
Canadian Journal of Mathematics / Journal canadien de mathématiques     Hybrid Journal  
Canadian Journal of Science, Mathematics and Technology Education     Hybrid Journal   (Followers: 20)
Canadian Mathematical Bulletin     Hybrid Journal  
Carpathian Mathematical Publications     Open Access  
Catalysis in Industry     Hybrid Journal  
CAUCHY     Open Access   (Followers: 1)
CEAS Space Journal     Hybrid Journal   (Followers: 6)
CHANCE     Hybrid Journal   (Followers: 5)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 1)
Chaos, Solitons & Fractals : X     Open Access   (Followers: 1)
ChemSusChem     Hybrid Journal   (Followers: 7)
Chinese Annals of Mathematics, Series B     Hybrid Journal  
Chinese Journal of Catalysis     Full-text available via subscription   (Followers: 2)
Chinese Journal of Mathematics     Open Access  
Ciencia     Open Access  
CODEE Journal     Open Access  
Cogent Mathematics     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 2)
Collectanea Mathematica     Hybrid Journal  
College Mathematics Journal     Hybrid Journal   (Followers: 3)
COMBINATORICA     Hybrid Journal  
Combinatorics, Probability and Computing     Hybrid Journal   (Followers: 4)
Combustion Theory and Modelling     Hybrid Journal   (Followers: 18)
Commentarii Mathematici Helvetici     Hybrid Journal   (Followers: 1)
Communications in Combinatorics and Optimization     Open Access  
Communications in Contemporary Mathematics     Hybrid Journal  
Communications in Mathematical Physics     Hybrid Journal   (Followers: 2)
Communications On Pure & Applied Mathematics     Hybrid Journal   (Followers: 6)
Complex Analysis and its Synergies     Open Access   (Followers: 2)
Complex Variables and Elliptic Equations: An International Journal     Hybrid Journal  
Compositio Mathematica     Full-text available via subscription   (Followers: 2)
Comptes Rendus : Mathematique     Open Access  
Computational and Applied Mathematics     Hybrid Journal   (Followers: 3)
Computational and Mathematical Methods     Hybrid Journal  
Computational and Mathematical Methods in Medicine     Open Access   (Followers: 2)
Computational and Mathematical Organization Theory     Hybrid Journal   (Followers: 1)
Computational Complexity     Hybrid Journal   (Followers: 5)
Computational Mathematics and Modeling     Hybrid Journal   (Followers: 8)
Computational Mechanics     Hybrid Journal   (Followers: 11)
Computational Methods and Function Theory     Hybrid Journal  
Computational Optimization and Applications     Hybrid Journal   (Followers: 9)
Computers & Mathematics with Applications     Full-text available via subscription   (Followers: 9)
Confluentes Mathematici     Hybrid Journal  
Constructive Mathematical Analysis     Open Access  
Contributions to Discrete Mathematics     Open Access  
Contributions to Game Theory and Management     Open Access  
COSMOS     Hybrid Journal   (Followers: 1)
Cross Section     Full-text available via subscription   (Followers: 1)
Cryptography and Communications     Hybrid Journal   (Followers: 11)
Cuadernos de Investigación y Formación en Educación Matemática     Open Access  
Cubo. A Mathematical Journal     Open Access  
Current Research in Biostatistics     Open Access   (Followers: 8)
Czechoslovak Mathematical Journal     Hybrid Journal  
Daya Matematis : Jurnal Inovasi Pendidikan Matematika     Open Access  
Demographic Research     Open Access   (Followers: 14)
Design Journal : An International Journal for All Aspects of Design     Hybrid Journal   (Followers: 33)
Desimal : Jurnal Matematika     Open Access  
Dhaka University Journal of Science     Open Access  
Differential Equations and Dynamical Systems     Hybrid Journal   (Followers: 2)
Differentsial'nye Uravneniya     Open Access  
Digital Experiences in Mathematics Education     Hybrid Journal   (Followers: 3)
Discrete Mathematics     Hybrid Journal   (Followers: 8)
Discrete Mathematics & Theoretical Computer Science     Open Access   (Followers: 1)
Discrete Mathematics, Algorithms and Applications     Hybrid Journal   (Followers: 2)
Discussiones Mathematicae - General Algebra and Applications     Open Access  
Discussiones Mathematicae Graph Theory     Open Access   (Followers: 1)
Diskretnaya Matematika     Full-text available via subscription  
Doklady Akademii Nauk     Open Access  
Doklady Mathematics     Hybrid Journal  
Eco Matemático     Open Access  
Econometrics     Open Access   (Followers: 2)

        1 2 3 4 | Last

Similar Journals
Journal Cover
Calculus of Variations and Partial Differential Equations
Journal Prestige (SJR): 3.352
Citation Impact (citeScore): 2
Number of Followers: 0  
 
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 1432-0835 - ISSN (Online) 0944-2669
Published by Springer-Verlag Homepage  [2469 journals]
  • Stable determination of an elastic medium scatterer by a single far-field
           measurement and beyond

    • Free pre-print version: Loading...

      Abstract: Abstract We are concerned with the time-harmonic elastic scattering due to an inhomogeneous elastic material inclusion located inside a uniformly homogeneous isotropic medium. We establish a sharp stability estimate of logarithmic type in determining the support of the elastic scatterer, independent of its material content, by a single far-field measurement when the support is a convex polyhedral domain in \({\mathbb {R}}^n\) , \(n=2,3\) . Our argument in establishing the stability result is localized around a corner of the medium scatterer. This enables us to further establish a byproduct result by proving that if a generic medium scatterer, not necessary to be a polyhedral shape, possesses a corner, then there exists a positive lower bound of the scattered far-field patterns. The latter result indicates that if an elastic material object possesses a corner on its support, then it scatters every incident wave stably and invisibility phenomenon does not occur.
      PubDate: 2022-06-24
       
  • A flow approach to the generalized Loewner-Nirenberg problem of the
           $$\sigma _k$$ σ k -Ricci equation

    • Free pre-print version: Loading...

      Abstract: Abstract We introduce a flow approach to the generalized Loewner-Nirenberg problem (1.5)-(1.7) of the \(\sigma _k\) -Ricci equation on a compact manifold \((M^n,g)\) with boundary. We prove that for initial data \(u_0\in C^{4,\alpha }(M)\) which is a subsolution to the \(\sigma _k\) -Ricci equation (1.5), the Cauchy-Dirichlet problem (3.1)-(3.3) has a unique solution u which converges in \(C^4_{loc}(M^{\circ })\) to the solution \(u_{\infty }\) of the problem (1.5)-(1.7), as \(t\rightarrow \infty \) .
      PubDate: 2022-06-24
       
  • Domain walls in the coupled Gross–Pitaevskii equations with the
           harmonic potential

    • Free pre-print version: Loading...

      Abstract: Abstract We study the existence and variational characterization of steady states in a coupled system of Gross–Pitaevskii equations modeling two-component Bose-Einstein condensates with the magnetic field trapping. The limit with no trapping has been the subject of recent works where domain walls have been constructed and several properties, including their orbital stability have been derived. Here we focus on the full model with the harmonic trapping potential and characterize minimizers according to the value of the coupling parameter \(\gamma \) . We first establish a rigorous connection between the two problems in the Thomas-Fermi limit via \(\Gamma \) -convergence. Then, we identify the ranges of \(\gamma \) for which either the symmetric states \((\gamma < 1)\) or the uncoupled states \((\gamma > 1)\) are minimizers. Domain walls arise as minimizers in a subspace of the energy space with a certain symmetry for some \(\gamma > 1\) . We study bifurcation of the domain walls and furthermore give numerical illustrations of our results.
      PubDate: 2022-06-22
       
  • Minimal measures on the level sets below Mañé critical value

    • Free pre-print version: Loading...

      Abstract: Abstract Minimal measure was introduced for positive definite Lagrangian systems to study their dynamics. For autonomous system, the support lies in the level set of the Hamiltonian not below the Mañé critical value. It is found in this paper that, for mechanical system, there also exist some minimal measures on the level sets below the Mañé critical value.
      PubDate: 2022-06-22
       
  • $$L^\infty $$ L ∞ -estimates in optimal transport for non quadratic
           costs

    • Free pre-print version: Loading...

      Abstract: Abstract For cost functions \(c(x,y)=h(x-y)\) , with \(h\in C^2\left( {{\mathbb {R}}}^n\setminus \{0\}\right) \cap C^1\left( {{\mathbb {R}}}^n\right) \) homogeneous of degree \(p>1\) , we show \(L^\infty \) -estimates of \(Tx-x\) on balls, where T is an h-monotone map. Estimates for the interpolating mappings \(T_t=t(T-I)+I\) are deduced from this.
      PubDate: 2022-06-22
       
  • On $$W^{2,p}$$ W 2 , p -estimates for solutions of obstacle problems for
           fully nonlinear elliptic equations with oblique boundary conditions

    • Free pre-print version: Loading...

      Abstract: Abstract This paper concerns fully nonlinear elliptic obstacle problems with oblique boundary conditions. We investigate the existence, uniqueness and \(W^{2,p}\) -regularity results by finding approximate non-obstacle problems with the same oblique boundary condition and then making a suitable limiting process.
      PubDate: 2022-06-22
       
  • On the cauchy problem of 3D compressible, viscous, heat-conductive
           navier-stokes-Poisson equations subject to large and non-flat doping
           profile

    • Free pre-print version: Loading...

      Abstract: Abstract In this paper, we study an initial value problem of the Navier-Stokes-Poisson equations for compressible, viscous, heat-conducting flows on the whole space \(\mathrm{{{\mathbb {R}}}^3}\) . The global well-posedness of strong solutions subject to large and non-flat doping profile is established. The initial data is of small energy but possible large oscillations, and the initial density is allowed to contain vacuum states.
      PubDate: 2022-06-22
       
  • Kellogg’s theorem for diffeomophic minimizers of Dirichlet energy
           between doubly connected Riemann surfaces

    • Free pre-print version: Loading...

      Abstract: Abstract We extend the celebrated theorem of Kellogg for conformal diffeomorphisms to the minimizers of Dirichlet energy. Namely we prove that a diffeomorphic minimizer of Dirichlet energy of Sobolev mappings between doubly connected Riemannian surfaces \(({\mathbb {X}},\sigma )\) and \(({\mathbb {Y}},\rho )\) having \({\mathscr {C}}^{n,\alpha }\) boundary, \(0<\alpha <1\) , is \({\mathscr {C}}^{n,\alpha }\) up to the boundary, provided the metric \(\rho \) is smooth enough. Here n is a positive integer. It is crucial that every diffeomorphic minimizer of Dirichlet energy is a harmonic mapping with a very special Hopf differential and this fact is used in the proof. This improves and extends a recent result by the author and Lamel in Kalaj and Lamel (Math Ann 377:1643–1672, 2020), where the authors proved a similar result for doubly-connected domains in the complex plane but for \(\alpha '\) which is \(\le \alpha \) and \(\rho \equiv 1\) . This is a complementary result of an existence result proved by T. Iwaniec et al. in Iwaniec et al. (Invent Math 186:667–707, 2011) and the author in Kalaj (Var Partial Differ Equ 51:465–494, 2014)
      PubDate: 2022-06-22
       
  • Weight metamorphosis of varifolds and the LDDMM-Fisher-Rao metric

    • Free pre-print version: Loading...

      Abstract: Abstract This paper introduces and studies a metamorphosis framework for geometric measures known as varifolds, which extends the diffeomorphic registration model for objects such as curves, surfaces and measures by complementing diffeomorphic deformations with a transformation process on the varifold weights. We consider two classes of cost functionals to penalize those combined transformations, in particular the LDDMM-Fisher-Rao energy which, as we show, leads to a well-defined Riemannian metric on the space of varifolds with existence of corresponding geodesics. We further introduce relaxed formulations of the respective optimal control problems, study their well-posedness and derive optimality conditions for the solutions. From these, we propose a numerical approach to compute optimal metamorphoses between discrete varifolds and illustrate the interest of this model in the situation of partially missing data.
      PubDate: 2022-06-22
       
  • Boundary regularity estimates in Hölder spaces with variable exponent

    • Free pre-print version: Loading...

      Abstract: Abstract We present a general blow-up technique to obtain local regularity estimates for solutions, and their derivatives, of second order elliptic equations in divergence form in Hölder spaces with variable exponent. The procedure allows to extend the estimates up to a portion of the boundary where Dirichlet or Neumann boundary conditions are prescribed and produces a Schauder theory for partial derivatives of solutions of any order \(k\in {\mathbb {N}}\) . The strategy relies on the construction of a class of suitable regularizing problems and an approximation argument. The given data of the problem are taken in Hölder and Lebesgue spaces, both with variable exponent.
      PubDate: 2022-06-22
       
  • Partial existence result for homogeneous quasilinear parabolic problems
           beyond the duality pairing

    • Free pre-print version: Loading...

      Abstract: Abstract In this paper, we study the existence of distributional solutions solving (1.3) on a bounded domain \(\Omega \) satisfying a uniform capacity density condition where the nonlinear structure \(\mathcal {A}(x,t,\nabla u)\) is modelled after the standard parabolic p-Laplace operator. In this regard, we need to prove a priori estimates for the gradient of the solution below the natural exponent and a higher integrability result for very weak solutions at the initial boundary. The elliptic counterpart to these two estimates is fairly well developed over the past few decades, but no analogous theory exists in the quasilinear parabolic setting. Two important features of the estimates proved here are that they are non-perturbative in nature and we are able to take non-zero boundary data. As a consequence, our a priori estimates are new even for the heat equation on bounded domains. This partial existence result is a nontrivial extension of the existence theory of very weak solutions from the elliptic setting to the quasilinear parabolic setting. Even though we only prove partial existence result, nevertheless we establish the necessary framework that when proved would lead to obtaining the full result for the homogeneous problem.
      PubDate: 2022-06-18
       
  • Limit profiles for singularly perturbed Choquard equations with local
           repulsion

    • Free pre-print version: Loading...

      Abstract: Abstract We study Choquard type equation of the form where \(N\ge 3\) , \(I_\alpha \) is the Riesz potential with \(\alpha \in (0,N)\) , \(p>1\) , \(q>2\) and \(\varepsilon \ge 0\) . Equations of this type describe collective behaviour of self-interacting many-body systems. The nonlocal nonlinear term represents long-range attraction while the local nonlinear term represents short-range repulsion. In the first part of the paper for a nearly optimal range of parameters we prove the existence and study regularity and qualitative properties of positive groundstates of \((P_0)\) and of \((P_\varepsilon )\) with \(\varepsilon >0\) . We also study the existence of a compactly supported groundstate for an integral Thomas–Fermi type equation associated to \((P_{\varepsilon })\) . In the second part of the paper, for \(\varepsilon \rightarrow 0\) we identify six different asymptotic regimes and provide a characterisation of the limit profiles of the groundstates of \((P_\varepsilon )\) in each of the regimes. We also outline three different asymptotic regimes in the case \(\varepsilon \rightarrow \infty \) . In one of the asymptotic regimes positive groundstates of \((P_\varepsilon )\) converge to a compactly supported Thomas–Fermi limit profile. This is a new and purely nonlocal phenomenon that can not be observed in the local prototype case of \((P_\varepsilon )\) with \(\alpha =0\) . In particular, this provides a justification for the Thomas–Fermi approximation in astrophysical models of self-gravitating Bose–Einstein condensate.
      PubDate: 2022-06-18
       
  • Scattering for the non-radial inhomogenous biharmonic NLS equation

    • Free pre-print version: Loading...

      Abstract: Abstract We consider the focusing inhomogeneous biharmonic nonlinear Schrödinger equation in \(H^2(\mathbb {R}^N)\) , $$\begin{aligned} iu_t + \Delta ^2 u - x ^{-b} u ^{\alpha }u=0, \end{aligned}$$ when \(b > 0\) and \(N \ge 5\) . We first obtain a small data global result in \(H^2\) , which, in the five-dimensional case, improves a previous result from Pastor and the second author. In the sequel, we show the main result, scattering below the mass-energy threshold in the intercritical case, that is, \(\frac{8-2b}{N}< \alpha <\frac{8-2b}{N-4}\) , without assuming radiality of the initial data. The proof combines the decay of the nonlinearity with Virial-Morawetz-type estimates to avoid the radial assumption, allowing for a much simpler proof than the Kenig-Merle roadmap.
      PubDate: 2022-06-14
       
  • Nonlinear approximation of 3D smectic liquid crystals: sharp lower bound
           and compactness

    • Free pre-print version: Loading...

      Abstract: Abstract We consider the 3D smectic energy $$\begin{aligned} {\mathcal {E}}_{\epsilon }\left( u\right) =\frac{1}{2}\int _{\Omega }\frac{1}{\varepsilon } \left( \partial _{z}u-\frac{(\partial _{x}u)^{2}+(\partial _{y}u)^{2}}{2}\right) ^{2} +\varepsilon \left( \partial _{x}^{2}u+\partial _{y}^{2}u\right) ^{2}dx\,dy\,dz. \end{aligned}$$ The model contains as a special case the well-known 2D Aviles-Giga model. We prove a sharp lower bound on \({\mathcal {E}}_{\varepsilon }\) as \(\varepsilon \rightarrow 0\) by introducing 3D analogues of the Jin–Kohn entropies Jin and Kohn (J Nonlinear Sci 10:355–390, 2000). The sharp bound corresponds to an equipartition of energy between the bending and compression strains and was previously demonstrated in the physics literature only when the approximate Gaussian curvature of each smectic layer vanishes. Also, for \(\varepsilon _{n}\rightarrow 0\) and an energy-bounded sequence \(\{u_n \}\) with \(\Vert \nabla u_n\Vert _{L^{p}(\Omega )},\, \Vert \nabla u_n\Vert _{L^2(\partial \Omega )}\le C\) for some \(p>6\) , we obtain compactness of \(\nabla u_{n}\) in \(L^{2}\) assuming that \(\Delta _{xy}u_{n}\) has constant sign for each n.
      PubDate: 2022-06-14
       
  • Monotonicity of positive solutions to quasilinear elliptic equations in
           half-spaces with a changing-sign nonlinearity

    • Free pre-print version: Loading...

      Abstract: Abstract In this paper we prove the monotonicity of positive solutions to \( -\Delta _p u = f(u) \) in half-spaces under zero Dirichlet boundary conditions, for \((2N+2)/(N+2)< p < 2\) and for a general class of regular changing-sign nonlinearities f. The techniques used in the proof of the main result are based on a fine use of comparison and maximum principles and on an adaptation of the celebrated moving plane method to quasilinear elliptic equations in unbounded domains.
      PubDate: 2022-06-14
       
  • Reducibility of quantum harmonic oscillator on $$\mathbb {R}^d$$ R d
           perturbed by a quasi: periodic potential with logarithmic decay

    • Free pre-print version: Loading...

      Abstract: Abstract We prove the reducibility of quantum harmonic oscillators in \({\mathbb {R}}^d\) perturbed by a quasi-periodic in time potential \(V(x,\omega t)\) with \(\textit{logarithmic decay}\) . By a new estimate built for solving the homological equation we improve the reducibility result by Grébert-Paturel(Annales de la Faculté des sciences de Toulouse : Mathématiques. \(\mathbf{28} \) , 2019).
      PubDate: 2022-06-14
       
  • Critical Hardy inequality on the half-space via the harmonic
           transplantation

    • Free pre-print version: Loading...

      Abstract: Abstract We prove a critical Hardy inequality on the half-space \({\mathbb {R}}^N_+\) by using the harmonic transplantation for functions in \({\dot{W}}_0^{1,N}({\mathbb {R}}^N_+)\) . Also we give an improvement of the subcritical Hardy inequality on \({\dot{W}}_0^{1,p}({\mathbb {R}}^N_+)\) for \(p \in [2, N)\) , which converges to the critical Hardy inequality when \(p \nearrow N\) . Sobolev type inequalities are also discussed.
      PubDate: 2022-06-14
       
  • Classification of solutions for some elliptic system

    • Free pre-print version: Loading...

      Abstract: Abstract In this paper, we classify the solution of the following elliptic system $$\begin{aligned} \left\{ \begin{array}{ll} \displaystyle -\Delta u(x)=e^{3v(x)}, &{}\quad x\in {\mathbb {R}}^4, \\ \\ \displaystyle (-\Delta )^2v(x)=u(x)^4, &{}\quad x\in {\mathbb {R}}^4. \end{array} \right. \end{aligned}$$ Under some assumptions, we will show that the solution has the following form $$\begin{aligned} u(x)=\frac{C_1(\varepsilon )}{\varepsilon ^2+ x-x_0 ^2},\ v(x)=\ln \frac{C_2(\varepsilon )}{\varepsilon ^2+ x-x_0 ^2}, \end{aligned}$$ where \(C_1,C_2\) are two positive constants depending only on \(\varepsilon \) and \(x_0\) is a fixed point in \({\mathbb {R}}^4.\)
      PubDate: 2022-06-10
       
  • Global Existence, Regularity and Boundedness in a Higher-dimensional
           Chemotaxis-Navier-Stokes System with Nonlinear Diffusion and General
           Sensitivity

    • Free pre-print version: Loading...

      Abstract: Abstract We consider an incompressible chemotaxis-Navier-Stokes system with nonlinear diffusion and rotational flux $$\begin{aligned} \left\{ \begin{array}{l} n_t+u\cdot \nabla n=\Delta n^m-\nabla \cdot (nS(x,n,c)\cdot \nabla c),\quad x\in \Omega , t>0,\\ c_t+u\cdot \nabla c=\Delta c-nc,\quad x\in \Omega , t>0,\\ u_t+\kappa (u \cdot \nabla )u+\nabla P=\Delta u+n\nabla \phi ,\quad x\in \Omega , t>0,\\ \nabla \cdot u=0,\quad x\in \Omega , t>0\\ \end{array}\right. \end{aligned}$$ in a bounded domain \(\Omega \subset {\mathbb {R}}^N(N=2,3)\) with smooth boundary \(\partial \Omega \) , where \(\kappa \in {\mathbb {R}}\) . The chemotaxtic sensitivity S is a given tensor-valued function fulfilling \( S(x,n,c) \le S_0(c)\) for all \((x,n,c)\in {\bar{\Omega }} \times [0, \infty )\times [0, \infty )\) with \(S_0(c)\) nondecreasing on \([0,\infty )\) . By introducing some new methods (see Sect. 4 and Sect. 5), we prove that under the condition \(m >1\) and some other proper regularity hypotheses on initial data, the corresponding initial-boundary problem possesses at least one global weak solution. The present work also shows that the weak solution could be bounded provided that \(N= 2\) . Since S is tensor-valued, it is easy to see that the restriction on m here is optimal, which answers the left question in Bellomo-Belloquid-Tao-Winkler (Math Models Methods Appl Sci 25:1663–1763, 2015) and Tao-Winkler (Ann Inst H Poincaré Anal Non Linéaire 30:157–178, 2013). And obviously, this work improves previous results of several other authors (see Remark 1.1).
      PubDate: 2022-06-10
       
  • Generic existence of multiplicity-1 minmax minimal hypersurfaces via
           Allen–Cahn

    • Free pre-print version: Loading...

      Abstract: Abstract In Guaraco (J. Differential Geom. 108(1):91–133, 2018) a new proof was given of the existence of a closed minimal hypersurface in a compact Riemannian manifold \(N^{n+1}\) with \(n\ge 2\) . This was achieved by employing an Allen–Cahn approximation scheme and a one-parameter minmax for the Allen–Cahn energy (relying on works by Hutchinson, Tonegawa, Wickramasekera to pass to the limit as the Allen-Cahn parameter tends to 0). The minimal hypersurface obtained may a priori carry a locally constant integer multiplicity. Here we modify the minmax construction of Guaraco (J. Differential Geom. 108(1):91–133, 2018), by allowing an initial freedom on the choice of the valley points between which the mountain pass construction is carried out, and then optimising over said choice. We then prove that, when \(2\le n\le 6\) and the metric is bumpy, this minmax leads to a (smooth closed) minimal hypersurface with multiplicity 1. (When \(n=2\) this conclusion also follows from Chodosh and Mantoulidis (Ann. Math. 191(1):213–328, 2020).) As immediate corollary we obtain that every compact Riemannian manifold of dimension \(n+1\) , \(2\le n\le 6\) , endowed with a bumpy metric, admits a two-sided smooth closed minimal hypersurface (this existence conclusion also follows from Zhou X (Ann. Math. (2), 192(3):767–820, 2020) for minmax constructions via Almgren–Pitts theory).
      PubDate: 2022-06-10
       
 
JournalTOCs
School of Mathematical and Computer Sciences
Heriot-Watt University
Edinburgh, EH14 4AS, UK
Email: journaltocs@hw.ac.uk
Tel: +00 44 (0)131 4513762
 


Your IP address: 44.192.65.228
 
Home (Search)
API
About JournalTOCs
News (blog, publications)
JournalTOCs on Twitter   JournalTOCs on Facebook

JournalTOCs © 2009-