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Publisher: Springer-Verlag (Total: 2350 journals)

 Annali di Matematica Pura ed Applicata   [SJR: 1.167]   [H-I: 26]   [1 followers]  Follow         Hybrid journal (It can contain Open Access articles)    ISSN (Print) 1618-1891 - ISSN (Online) 0373-3114    Published by Springer-Verlag  [2350 journals]
• On fractional p -Laplacian parabolic problem with general data
• Authors: B. Abdellaoui; A. Attar; R. Bentifour; I. Peral
Pages: 329 - 356
Abstract: In this article, the problem to be studied is the following \begin{aligned} (P) \left\{ \begin{array}{llll} u_t+(-\Delta ^s_{p}) u = f(x,t) &{}\quad \text { in } \Omega _{T}\equiv \Omega \times (0,T), \\ u = 0 &{}\quad \text { in }({\mathbb {R}}^N{\setminus }\Omega ) \times (0,T), \\ u(x,0) = u(x) &{}\quad \text{ in } \Omega , \end{array} \right. \end{aligned} where $$\Omega$$ is a bounded domain and $$(-\Delta ^s_{p})$$ is the fractional p-Laplacian operator defined by \begin{aligned} (-\Delta ^s_{p})\, u(x,t):=P.V\int _{{\mathbb {R}}^N} \,\dfrac{ u(x,t)-u(y,t) ^{p-2}(u(x,t)-u(y,t))}{ x-y ^{N+ps}} \,\mathrm{d}y \end{aligned} with $$1<p<N$$ , $$s\in (0,1)$$ and $$f, u_0$$ being measurable functions. The main goal of this work is to prove that if $$(f,u_0)\in L^1(\Omega _T)\times L^1(\Omega )$$ , problem (P) has a weak solution with suitable regularity. In addition, if $$f_0, u_0$$ are nonnegative, we show that the problem above has a nonnegative entropy solution. In the case of nonnegative data, we give also some quantitative and qualitative properties of the solution according the values of p.
PubDate: 2018-04-01
DOI: 10.1007/s10231-017-0682-z
Issue No: Vol. 197, No. 2 (2018)

• Second-order Lagrangians admitting a first-order Hamiltonian formalism
• Authors: E. Rosado María; J. Muñoz Masqué
Pages: 357 - 397
Abstract: Second-order Lagrangian densities admitting a first-order Hamiltonian formalism are studied; namely, (1) for each second-order Lagrangian density on an arbitrary fibred manifold $$p:E\rightarrow N$$ the Poincaré–Cartan form of which is projectable onto $$J^1E$$ , by using a new notion of regularity previously introduced, a first-order Hamiltonian formalism is developed for such a class of variational problems; (2) the existence of first-order equivalent Lagrangians is discussed from a local point of view as well as global; (3) this formalism is then applied to classical Hilbert–Einstein Lagrangian and a generalization of the BF theory. The results suggest that the class of problems studied is a natural variational setting for GR.
PubDate: 2018-04-01
DOI: 10.1007/s10231-017-0683-y
Issue No: Vol. 197, No. 2 (2018)

• Examples of foliations with infinite dimensional special cohomology
• Authors: Andrzej Czarnecki; Paweł Raźny
Pages: 399 - 409
Abstract: We present two examples of foliations with infinite dimensional basic symplectic and complex cohomologies, along with a general sufficient condition for such phenomena. This puts restrictions on possible generalisations of several finiteness results from Riemannian foliations to any broader class. The examples are also noteworthy for the unusual behaviour of their basic de Rham cohomology.
PubDate: 2018-04-01
DOI: 10.1007/s10231-017-0684-x
Issue No: Vol. 197, No. 2 (2018)

• The Frölicher–Nijenhuis bracket and the geometry of $$G_2$$ G 2 -and
Spin(7)-manifolds
• Authors: Kotaro Kawai; Hông Vân Lê; Lorenz Schwachhöfer
Pages: 411 - 432
Abstract: We extend the characterization of the integrability of an almost complex structure J on differentiable manifolds via the vanishing of the Frölicher–Nijenhuis bracket $$[J, J]^{FN}$$ to an analogous characterization of torsion-free $$G_2$$ -structures and torsion-free $$\text{Spin(7) }$$ -structures. We also explain the Fernández–Gray classification of $$G_2$$ -structures and the Fernández classification of $$\text{Spin(7) }$$ -structures in terms of the Frölicher–Nijenhuis bracket.
PubDate: 2018-04-01
DOI: 10.1007/s10231-017-0685-9
Issue No: Vol. 197, No. 2 (2018)

• Higher-dimensional study of extensions via torsors
• Authors: Cristiana Bertolin; Ahmet Emin Tatar
Pages: 433 - 468
Abstract: Let $$\mathbf {S}$$ be a site. First we define the 3-category of torsors under a Picard $$\mathbf {S}$$ -2-stack and we compute its homotopy groups. Using calculus of fractions, we define also a pure algebraic analogue of the 3-category of torsors under a Picard $$\mathbf {S}$$ -2-stack. Then we describe extensions of Picard $$\mathbf {S}$$ -2-stacks as torsors endowed with a group law on the fibers. As a consequence of such a description, we show that any Picard $$\mathbf {S}$$ -2-stack admits a canonical free partial left resolution that we compute explicitly. Moreover, we get an explicit right resolution of the 3-category of extensions of Picard $$\mathbf {S}$$ -2-stacks in terms of 3-categories of torsors. Using the homological interpretation of Picard $$\mathbf {S}$$ -2-stacks, we rewrite this three categorical dimensions higher right resolution in the derived category $$\mathcal {D}(\mathbf {S})$$ of abelian sheaves on $$\mathbf {S}$$ .
PubDate: 2018-04-01
DOI: 10.1007/s10231-017-0686-8
Issue No: Vol. 197, No. 2 (2018)

• An algorithm to estimate the vertices of a tetrahedron from uniform random
points inside
• Authors: Alina-Daniela Vîlcu; Gabriel-Eduard Vîlcu
Pages: 487 - 500
Abstract: In this paper, we give an algorithm to infer the positions of the vertices of an unknown tetrahedron, given a sample of points which are uniformly distributed within the tetrahedron. The accuracy of the algorithm is demonstrated using some numerical experiments.
PubDate: 2018-04-01
DOI: 10.1007/s10231-017-0688-6
Issue No: Vol. 197, No. 2 (2018)

• Optimal partition problems for the fractional Laplacian
• Authors: Antonella Ritorto
Pages: 501 - 516
Abstract: In this work, we prove an existence result for an optimal partition problem of the form \begin{aligned} \min \{F_s(A_1,\ldots ,A_m):A_i \in {\mathcal {A}}_s, \, A_i\cap A_j =\emptyset \text{ for } i\ne j\}, \end{aligned} where $$F_s$$ is a cost functional with suitable assumptions of monotonicity and lower semicontinuity, $${\mathcal {A}}_s$$ is the class of admissible domains and the condition $$A_i\cap A_j =\emptyset$$ is understood in the sense of Gagliardo s-capacity, where $$0<s<1$$ . Examples of this type of problem are related to fractional eigenvalues. As the main outcome of this article, we prove some type of convergence of the s-minimizers to the minimizer of the problem with $$s=1$$ , studied in [5].
PubDate: 2018-04-01
DOI: 10.1007/s10231-017-0689-5
Issue No: Vol. 197, No. 2 (2018)

• Les cycles répulsifs bifurquent en chaîne
• Authors: François Berteloot
Pages: 517 - 520
Abstract: Nous remarquons que les bifurcations des cycles répulsifs d’endomorphismes holomorphes de $$\mathbb {P}^k$$ sont soumises à une alternative du type tout où rien. Cette observation est nouvelle, même en dimension $$k=1$$ .
PubDate: 2018-04-01
DOI: 10.1007/s10231-017-0690-z
Issue No: Vol. 197, No. 2 (2018)

• Well-posedness and Gevrey analyticity of the generalized Keller–Segel
system in critical Besov spaces
• Authors: Jihong Zhao
Pages: 521 - 548
Abstract: In this paper, we study the Cauchy problem for the generalized Keller–Segel system with the cell diffusion being ruled by fractional diffusion: \begin{aligned} {\left\{ \begin{array}{ll} \partial _{t}u+\Lambda ^{\alpha }u+\nabla \cdot (u\nabla \psi )=0 &{}\quad \text{ in }\ \ \mathbb {R}^n\times (0,\infty ),\\ -\Delta \psi =u &{}\quad \text{ in }\ \ \mathbb {R}^n\times (0,\infty ),\\ u(x,0)=u_0(x)\ \ &{}\quad \text{ in }\ \ \mathbb {R}^n. \end{array}\right. } \end{aligned} In the case $$1<\alpha \le 2$$ , we prove local well-posedness for any initial data and global well-posedness for small initial data in critical Besov spaces $$\dot{B}^{-\alpha +\frac{n}{p}}_{p,q}(\mathbb {R}^{n})$$ with $$1\le p<\infty$$ , $$1\le q\le \infty$$ , and analyticity of solutions for initial data $$u_{0}\in \dot{B}^{-\alpha +\frac{n}{p}}_{p,q}(\mathbb {R}^{n})$$ with $$1< p<\infty$$ , $$1\le q\le \infty$$ . Moreover the global existence and analyticity of solutions with small initial data in critical Besov spaces $$\dot{B}^{-\alpha }_{\infty ,1}(\mathbb {R}^{n})$$ is also established. In the limit case $$\alpha =1$$ , we prove global well-posedness for small initial data in critical Besov spaces $$\dot{B}^{-1+\frac{n}{p}}_{p,1}(\mathbb {R}^{n})$$ with $$1\le p<\infty$$ and $$\dot{B}^{-1}_{\infty ,1}(\mathbb {R}^{n})$$ and show analyticity of solutions for small initial data in $$\dot{B}^{-1+\frac{n}{p}}_{p,1}(\mathbb {R}^{n})$$ with $$1<p<\infty$$ and $$\dot{B}^{-1}_{\infty ,1}(\mathbb {R}^{n})$$ , respectively.
PubDate: 2018-04-01
DOI: 10.1007/s10231-017-0691-y
Issue No: Vol. 197, No. 2 (2018)

• The classical obstacle problem with coefficients in fractional Sobolev
spaces
• Authors: Francesco Geraci
Pages: 549 - 581
Abstract: We prove quasi-monotonicity formulae for classical obstacle-type problems with quadratic energies with coefficients in fractional Sobolev spaces, and a linear term with a Dini-type continuity property. These formulae are used to obtain the regularity of free-boundary points following the approaches by Caffarelli, Monneau and Weiss.
PubDate: 2018-04-01
DOI: 10.1007/s10231-017-0692-x
Issue No: Vol. 197, No. 2 (2018)

• Asymptotic analysis of a ferromagnetic Ising system with
“diffuse” interfacial energy
• Authors: Andrea Braides; Andrea Causin; Margherita Solci
Pages: 583 - 604
Abstract: We give an example of a one-dimensional scalar Ising-type energy with long-range interactions not satisfying standard decay conditions and which admits a continuum approximation finite for all functions u in $$BV((0,L),[-1,1])$$ and taking into account the total variation of u. The optimal discrete arrangements show a periodic pattern of interfaces. In this sense, the continuum energy is generated by “diffuse” microscopic interfacial energy. We also show that related minimum problems show boundary and size effects in dependence of L.
PubDate: 2018-04-01
DOI: 10.1007/s10231-017-0693-9
Issue No: Vol. 197, No. 2 (2018)

• A deviation inequality and quasi-ergodicity for absorbing Markov processes
• Authors: Jinwen Chen; Siqi Jian
Pages: 641 - 650
Abstract: In this note, we study quasi-ergodic behavior for killed Markov process. For symmetric stable processes, we derive a conditional deviation inequality for $$\int _0^tV(X_s)\hbox {d}s$$ for certain (unbounded) functions V. Then we apply it to prove a quasi $$L^1$$ -ergodic theorem for the killed process.
PubDate: 2018-04-01
DOI: 10.1007/s10231-017-0695-7
Issue No: Vol. 197, No. 2 (2018)

• Invariant almost complex structures on real flag manifolds
• Authors: Ana P. C. Freitas; Viviana del Barco; Luiz A. B. San Martin
Abstract: In this work, we study the existence of invariant almost complex structures on real flag manifolds associated to split real forms of complex simple Lie algebras. We show that, contrary to the complex case where the invariant almost complex structures are well known, some real flag manifolds do not admit such structures. We check which invariant almost complex structures are integrable and prove that only some flag manifolds of the Lie algebra $$C_{l}$$ admit complex structures.
PubDate: 2018-04-27
DOI: 10.1007/s10231-018-0751-y

• Global diffeomorphism of the Lagrangian flow-map for Pollard-like
solutions
Abstract: We present a rigorous analysis of the nonlinear surface waves in the presence of a zonal current under the effects of Earth’s rotation derived by Constantin and Monismith (J Fluid Mech 820:511–528, 2017). It is shown that the three-dimensional Lagrangian flow-map describing this exact solution is a global diffeomorphism, resulting in a flow description that is dynamically possible.
PubDate: 2018-04-27
DOI: 10.1007/s10231-018-0749-5

• Global-in-time existence results for the two-dimensional
Hasegawa–Wakatani equations
• Authors: Shintaro Kondo
Abstract: In order to describe the resistive drift wave turbulence appearing in nuclear fusion plasma, the Hasegawa–Wakatani (HW) equations were proposed in 1983. We consider the two-dimensional HW equations, which have numerous structures (that is, they explain the branching phenomenon in turbulent and zonal flow in a two-dimensional plasma) and the generalized HW equations that include temperature fluctuation. We prove the global-in-time existence of a unique strong solution to both the HW equations and the generalized HW equations in a two-dimensional domain with double periodic boundary conditions.
PubDate: 2018-04-25
DOI: 10.1007/s10231-018-0750-z

• Equivariant prequantization bundles on the space of connections and
characteristic classes
• Authors: Roberto Ferreiro Pérez
Abstract: We show how characteristic classes determine equivariant prequantization bundles over the space of connections on a principal bundle. These bundles are shown to generalize the Chern–Simons line bundles to arbitrary dimensions. Our result applies to arbitrary bundles, and we study the action of both the gauge group and the automorphisms group. The action of the elements in the connected component of the identity of the group generalizes known results in the literature. The action of the elements not connected with the identity is shown to be determined by a characteristic class by using differential characters and equivariant cohomology. We extend our results to the space of Riemannian metrics and the actions of diffeomorphisms. In dimension 2, a $$\Gamma _{M}$$ -equivariant prequantization bundle of the Weil–Petersson symplectic form on the Teichmüller space is obtained, where $$\Gamma _{M}$$ is the mapping class group of the surface M.
PubDate: 2018-04-24
DOI: 10.1007/s10231-018-0747-7

• Bounds on the tensor rank
• Authors: Edoardo Ballico; Alessandra Bernardi; Luca Chiantini; Elena Guardo
Abstract: We give a sufficient criterion for a lower bound of the cactus rank of a tensor. Then we refine that criterion in order to be able to give an explicit sufficient condition for a non-redundant decomposition of a tensor to be minimal and unique.
PubDate: 2018-04-24
DOI: 10.1007/s10231-018-0748-6

• On limits of triply periodic minimal surfaces
• Authors: Norio Ejiri; Shoichi Fujimori; Toshihiro Shoda
Abstract: In this paper, we introduce generic limits of triply periodic minimal surfaces and consider the genus-three case. We will prove that generic limits of such minimal surfaces consist of a one-parameter family of Karcher’s saddle towers and Rodríguez’ standard examples.
PubDate: 2018-04-12
DOI: 10.1007/s10231-018-0746-8

• On a Hecke-type functional equation with conductor $$\varvec{q=5}$$ q = 5
• Authors: J. Kaczorowski; A. Perelli
Abstract: We give a complete characterization of the solutions F(s) of the analog in the Selberg class of Hecke’s functional equation of conductor 5, namely \begin{aligned} \left( \frac{\sqrt{5}}{2\pi }\right) ^s \varGamma (s+\mu ) F(s) = \omega \left( \frac{\sqrt{5}}{2\pi }\right) ^{1-s} \varGamma (1-s+\overline{\mu }) \overline{F(1-\overline{s})} \end{aligned} with $$\mathfrak {R}{\mu }\ge 0$$ and $$\omega =1$$ . The proof is based on several results from our theory of nonlinear twists of L-functions, applied to obtain a full description of the Euler factor of F(s) at $$p=2$$ , and then on some ideas from a 1995 paper by J. B. Conrey and D. W. Farmer on converse theorems for Euler products.
PubDate: 2018-04-11
DOI: 10.1007/s10231-018-0744-x

• Uniform boundedness of the attractor in $$H^2$$ H 2 of a non-autonomous
epidemiological system
• Authors: María Anguiano
Abstract: In this paper, we prove the uniform boundedness of the pullback attractor of a non-autonomous SIR (susceptible, infected, recovered) model from epidemiology considered in Anguiano and Kloeden (Commun Pure Appl Anal 13(1):157–173, 2014). We prove two uniform bounds of this pullback attractor, firstly in the norm $$H_0^1$$ and later, under appropriate additional assumptions, in the norm $$H^2$$ .
PubDate: 2018-04-09
DOI: 10.1007/s10231-018-0745-9

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