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 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  [2335 journals]
• Stability for quantitative photoacoustic tomographywith well-chosen
illuminations
• Authors: Giovanni Alessandrini; Michele Di Cristo; Elisa Francini; Sergio Vessella
Pages: 395 - 406
Abstract: Abstract We treat the stability issue for the three-dimensional inverse imaging modality called quantitative photoacoustic tomography. We provide universal choices of the illuminations which enable to recover, in a Hölder stable fashion, the diffusion and absorption coefficients from the interior pressure data. With such choices of illuminations we do not need the nondegeneracy conditions commonly used in previous studies, which are difficult to be verified a priori.
PubDate: 2017-04-01
DOI: 10.1007/s10231-016-0577-4
Issue No: Vol. 196, No. 2 (2017)

• Submanifolds with nonpositive extrinsic curvature
• Authors: Samuel Canevari; Guilherme Machado de Freitas; Fernando Manfio
Pages: 407 - 426
Abstract: Abstract We prove that complete submanifolds, on which the weak Omori-Yau maximum principle for the Hessian holds, with low codimension and bounded by cylinders of small radius must have points rich in large positive extrinsic curvature. The lower the codimension is, the richer such points are. The smaller the radius is, the larger such curvatures are. This work unifies and generalizes several previous results on submanifolds with nonpositive extrinsic curvature.
PubDate: 2017-04-01
DOI: 10.1007/s10231-016-0578-3
Issue No: Vol. 196, No. 2 (2017)

• Asymptotically linear fractional p -Laplacian equations
• Authors: Rossella Bartolo; Giovanni Molica Bisci
Pages: 427 - 442
Abstract: Abstract In this paper we study the multiplicity of weak solutions to (possibly resonant) nonlocal equations involving the fractional p-Laplacian operator. More precisely, we consider a Dirichlet problem driven by the fractional p-Laplacian operator and involving a subcritical nonlinear term which does not satisfy the technical Ambrosetti–Rabinowitz condition. By framing this problem in an appropriate variational setting, we prove a multiplicity theorem.
PubDate: 2017-04-01
DOI: 10.1007/s10231-016-0579-2
Issue No: Vol. 196, No. 2 (2017)

• Stability of odd periodic solutions in a resonant oscillator
• Authors: Daniel Núñez; Andrés Rivera; Gian Rossodivita
Pages: 443 - 455
Abstract: Abstract We obtain an odd $$2\pi$$ -periodic solution $$\varphi$$ in a driven differential equation \begin{aligned} \ddot{x}+g(x)=\varepsilon p(t), \end{aligned} where g and p are odd smooth functions with $$g^{\prime }(0)=n^{2}$$ for some $$n\in \mathbb {N}$$ and $$g^{\prime \prime \prime }(0)\ne 0$$ . The periodic solution $$\varphi$$ is obtained by continuation of the equilibrium $$x\equiv 0$$ of the unperturbed problem $$(\varepsilon =0)$$ for small $$\varepsilon$$ . In order to prove this result, we establish an extension of a Loud’s version of the implicit function theorem at rank 0. Moreover, we present sufficient conditions for the existence of one or three odd $$2\pi$$ -periodic continuations and also we give conditions for their linear stability.
PubDate: 2017-04-01
DOI: 10.1007/s10231-016-0580-9
Issue No: Vol. 196, No. 2 (2017)

• Extensions of degree $$p^\ell$$ p ℓ of a p -adic field
• Authors: Maria Rosaria Pati
Pages: 457 - 477
Abstract: Abstract Given a p-adic field K and a prime number $$\ell$$ , we count the total number of the isomorphism classes of $$p^\ell$$ -extensions of K having no intermediate fields. Moreover, for each group that can appear as Galois group of the normal closure of such an extension, we count the number of isomorphism classes that contain extensions whose normal closure has Galois group isomorphic to the given group. Finally, we determine the ramification groups and the discriminant of the composite of all $$p^\ell$$ -extensions of K with no intermediate fields. The principal tool is a result, proved at the beginning of the paper, which states that there is a one-to-one correspondence between the isomorphism classes of extensions of degree $$p^\ell$$ of K having no intermediate extensions and the irreducible H-submodules of dimension $$\ell$$ of $$F^*{/}{F^*}^p$$ , where F is the composite of certain fixed normal extensions of K and H is its Galois group over K.
PubDate: 2017-04-01
DOI: 10.1007/s10231-016-0581-8
Issue No: Vol. 196, No. 2 (2017)

• Superlinear Neumann problems with the p -Laplacian plus an indefinite
potential
• Authors: Genni Fragnelli; Dimitri Mugnai; Nikolaos S. Papageorgiou
Pages: 479 - 517
Abstract: Abstract We consider nonlinear Neumann problems driven by the p-Laplacian plus an indefinite potential and with a superlinear reaction which need not satisfy the Ambrosetti–Rabinowitz condition. First, we prove an existence theorem, and then, under stronger conditions on the reaction, we prove a multiplicity theorem producing three nontrivial solutions. Then, we examine parametric problems with competing nonlinearities (concave and convex terms). We show that for all small values of the parameter $$\lambda >0$$ , the problem has five nontrivial solutions and if $$p=2$$ (semilinear equation), there are six nontrivial solutions. Finally, we prove a bifurcation result describing the set of positive solutions as the parameter $$\lambda >0$$ varies.
PubDate: 2017-04-01
DOI: 10.1007/s10231-016-0582-7
Issue No: Vol. 196, No. 2 (2017)

• Algebraic approximation preserving dimension
• Authors: M. Ferrarotti; E. Fortuna; L. Wilson
Pages: 519 - 531
Abstract: Abstract We prove that each semialgebraic subset of $${\mathbb R}^n$$ of positive codimension can be locally approximated of any order by means of an algebraic set of the same dimension. As a consequence of previous results, algebraic approximation preserving dimension holds also for semianalytic sets.
PubDate: 2017-04-01
DOI: 10.1007/s10231-016-0583-6
Issue No: Vol. 196, No. 2 (2017)

• Comments on Sampson’s approach toward Hodge conjecture on Abelian
varieties
• Authors: Tuyen Trung Truong
Pages: 533 - 538
Abstract: Abstract Let A be an Abelian variety of dimension n. For $$0<p<2n$$ an odd integer, Sampson constructed a surjective homomorphism $$\pi {:}\,J^p(A)\rightarrow A$$ , where $$J^p(A)$$ is the higher Weil Jacobian variety of A. Let $${\widehat{\omega }}$$ be a fixed form in $$H^{1,1}(J^p(A),{\mathbb {Q}})$$ , and $$N=\dim (J^p(A))$$ . He observes that if the map $$\pi _*({\widehat{\omega }}^{N-p-1}\wedge .){:}\, H^{1,1}(J^p(A),{\mathbb {Q}})\rightarrow H^{n-p,n-p}(A,{\mathbb {Q}})$$ is injective, then the Hodge conjecture is true for A in bidegree (p, p). In this paper, we give some clarification of the approach and show that the map above is not injective except some special cases where the Hodge conjecture is already known. We propose a modified approach.
PubDate: 2017-04-01
DOI: 10.1007/s10231-016-0584-5
Issue No: Vol. 196, No. 2 (2017)

• Generalized fundamental matrices as Grassmann tensors
• Authors: Marina Bertolini; GianMario Besana; Cristina Turrini
Pages: 539 - 553
Abstract: Abstract Given two linear projections of maximal rank from $${\mathbb P}^{k}$$ to $${\mathbb P}^{h_1}$$ and $${\mathbb P}^{h_2},$$ with $$k\ge 3$$ and $$h_1+h_2\ge k+1,$$ the Grassmann tensor introduced by Hartley and Schaffalitzky (Int J Comput Vis 83(3):274–293, 2009. doi:10.1007/s11263-009-0225-1), turns out to be a generalized fundamental matrix. Such matrices are studied in detail and, in particular, their rank is computed. The dimension of the variety that parameterizes such matrices is also determined. An algorithmic application of the generalized fundamental matrix to projective reconstruction is described.
PubDate: 2017-04-01
DOI: 10.1007/s10231-016-0585-4
Issue No: Vol. 196, No. 2 (2017)

• Interior regularity of solutions of non-local equations in Sobolev and
Nikol’skii spaces
• Authors: Matteo Cozzi
Pages: 555 - 578
Abstract: Abstract We prove interior  $$H^{2 s - \varepsilon }$$ regularity for weak solutions of linear elliptic integro-differential equations close to the fractional s-Laplacian. The result is obtained via intermediate estimates in Nikol’skii spaces, which are in turn carried out by means of an appropriate modification of the classical translation method by Nirenberg.
PubDate: 2017-04-01
DOI: 10.1007/s10231-016-0586-3
Issue No: Vol. 196, No. 2 (2017)

• Hardy–Sobolev-type inequalities with monomial weights
• Authors: Hernán Castro
Pages: 579 - 598
Abstract: Abstract We give an elementary proof of a family of Hardy–Sobolev-type inequalities with monomial weights. As a corollary, we obtain a weighted trace inequality related to the fractional Laplacian.
PubDate: 2017-04-01
DOI: 10.1007/s10231-016-0587-2
Issue No: Vol. 196, No. 2 (2017)

• On critical exponents for Lane–Emden–Fowler-type equations with a
singular extremal operator
• Authors: Osiris González-Melendez; Alexander Quaas
Pages: 599 - 615
Abstract: Abstract In this article, we consider the nonlinear elliptic equation Here, $$\mathcal {M^{+}}_{\lambda , \Lambda }$$ denotes Pucci’s extremal operator with parameters $$\Lambda \ge \lambda > 0$$ and $$-1<\beta <0$$ . We prove the existence of a critical exponent $$p^{*}_+$$ that determines the range of $$p>1$$ for which we have the existence or nonexistence of a positive radial solution to $$(\star )$$ . In addition, we describe the solution set in terms of the parameter p and find two new critical exponents $$1<p^{*}_{+}<{\tilde{p}}_{\beta }$$ for the equation $$(\star )$$ , where the solution set sharply changes its qualitative properties when the value of p exceeds these critical exponents.
PubDate: 2017-04-01
DOI: 10.1007/s10231-016-0588-1
Issue No: Vol. 196, No. 2 (2017)

• Time periodic traveling curved fronts of bistable reaction–diffusion
equations in $${\mathbb {R}}^3$$ R 3
• Authors: Wei-Jie Sheng
Pages: 617 - 639
Abstract: Abstract This paper is concerned with the existence and stability of time periodic traveling curved fronts for reaction–diffusion equations with bistable nonlinearity in $${\mathbb {R}}^3$$ . We first study the existence and other qualitative properties of time periodic traveling fronts of polyhedral shape. Furthermore, for any given $$g\in C^{\infty }(S^1)$$ with $$\min \nolimits _{0\le \theta \le 2\pi }g(\theta )=0$$ that gives a convex bounded domain with smooth boundary of positive curvature everywhere, which is included in a sequence of convex polygons, we show that there exists a three-dimensional time periodic traveling front by taking the limit of the solutions corresponding to the convex polyhedrons as the number of the lateral surfaces goes to infinity.
PubDate: 2017-04-01
DOI: 10.1007/s10231-016-0589-0
Issue No: Vol. 196, No. 2 (2017)

• Globally stable quasistatic evolution for strain gradient plasticity
coupled with damage
• Authors: Vito Crismale
Pages: 641 - 685
Abstract: Abstract We consider evolutions for a material model which couples scalar damage with strain gradient plasticity, in small strain assumptions. For strain gradient plasticity, we follow the Gurtin–Anand formulation (J Mech Phys Solids 53:1624–1649, 2005). The aim of the present model is to account for different phenomena: On the one hand, the elastic stiffness reduces and the plastic yield surface shrinks due to material’s degradation, on the other hand the dislocation density affects the damage growth. The main result of this paper is the existence of a globally stable quasistatic evolution (in the so-called energetic formulation). Furthermore, we study the limit model as the strain gradient terms tend to zero. Under stronger regularity assumptions, we show that the evolutions converge to the ones for the coupled elastoplastic damage model studied in Crismale (ESAIM Control Optim Calc Var 22:883-912, 2016).
PubDate: 2017-04-01
DOI: 10.1007/s10231-016-0590-7
Issue No: Vol. 196, No. 2 (2017)

• Sobolev spaces of isometric immersions of arbitrary dimension and
co-dimension
Pages: 687 - 716
Abstract: Abstract We prove the $$C^{1}_{\mathrm{{loc}}}$$ regularity and developability of $$W^{2,p}_{\mathrm{{loc}}}$$ isometric immersions of n-dimensional flat domains into $${\mathbb {R}}^{n+k}$$ where $$p\ge \min \{2k, n\}$$ . We also prove similar rigidity and regularity results for scalar functions of n variables for which the rank of the Hessian matrix is a.e. bounded by some $$k<n$$ , again assuming $$W^{2,p}_{\mathrm{{loc}}}$$ regularity for $$p\ge \min \{2k,n\}$$ . In particular, this includes results about the degenerate Monge–Ampère equation, $$\mathrm{{det}} D^2 u = 0$$ , corresponding to the case $$k=n-1$$ .
PubDate: 2017-04-01
DOI: 10.1007/s10231-016-0591-6
Issue No: Vol. 196, No. 2 (2017)

• Periodic solutions of an asymptotically linear Dirac equation
• Authors: Yanheng Ding; Xiaoying Liu
Pages: 717 - 735
Abstract: Abstract Using the variational method, we investigate periodic solutions of a Dirac equation with asymptotically nonlinearity. The variational setting is established and the existence and multiplicity of periodic solutions are obtained.
PubDate: 2017-04-01
DOI: 10.1007/s10231-016-0592-5
Issue No: Vol. 196, No. 2 (2017)

• A Landau’s theorem in several complex variables
• Authors: Cinzia Bisi
Pages: 737 - 742
Abstract: Abstract In one complex variable, it is well known that if we consider the family of all holomorphic functions on the unit disc that fix the origin and with first derivative equal to 1 at the origin, then there exists a constant $$\rho$$ , independent of the functions, such that in the image of the unit disc of any of the functions of the family, there is a disc of universal radius $$\rho$$ . This is the so celebrated Landau’s theorem. Many counterexamples to an analogous result in several complex variables exist. In this paper, we introduce a class of holomorphic maps for which one can get a Landau’s theorem and a Brody–Zalcman theorem in several complex variables.
PubDate: 2017-04-01
DOI: 10.1007/s10231-016-0593-4
Issue No: Vol. 196, No. 2 (2017)

• Double loop algebras and elliptic root systems
• Authors: Kenji Iohara; Hiroshi Yamada
Pages: 743 - 771
Abstract: Abstract In this note, we describe an elliptic root system and elliptic Weyl group, due to Saito (Publ RIMS Kyoto Univ 21:75–179, 1985), from view point of double loop algebra and its group. A natural action of the double loop group will be introduced on a trivial $$\mathbb {C}^*$$ -bundle over the space of $$\overline{\partial }$$ -connections on a $$C^\infty$$ -trivial principal bundle over an elliptic curve that would be constructed from 2-dimensional central extension of a double loop algebra. The invariant theory of the elliptic Weyl group will be also discussed.
PubDate: 2017-04-01
DOI: 10.1007/s10231-016-0594-3
Issue No: Vol. 196, No. 2 (2017)

• On the cone of strong Kähler with torsion metrics
• Abstract: Abstract This paper examines special metrics on compact complex manifolds, and it is notably focused on the notion of super strong Kähler with torsion metric. This condition is related to the strong Kähler with torsion one in the same manner as the strongly Gauduchon condition is related to the Gauduchon one. Moreover, we provide sufficient and necessary conditions so that every strong Kähler with torsion metric on a compact complex manifold is in fact super strong Kähler with torsion. We prove that these conditions are verified on compact complex manifolds satisfying $$\partial \overline{\partial }$$ -lemma but not on 6-dimensional compact complex nilmanifolds.
PubDate: 2017-03-20

• Multiplicity of positive solutions for a class of fractional Schrödinger
equations via penalization method
• Authors: Vincenzo Ambrosio
Abstract: Abstract By using the penalization method and the Ljusternik–Schnirelmann theory, we investigate the multiplicity of positive solutions of the following fractional Schrödinger equation \begin{aligned} \varepsilon ^{2s}(-\Delta )^{s} u + V(x)u = f(u)\quad \text{ in } {\mathbb {R}}^{N} \end{aligned} where $$\varepsilon >0$$ is a parameter, $$s\in (0, 1)$$ , $$N>2s$$ , $$(-\Delta )^{s}$$ is the fractional Laplacian, V is a positive continuous potential with local minimum, and f is a superlinear function with subcritical growth. We also obtain a multiplicity result when $$f(u)= u ^{q-2}u+\lambda u ^{r-2}u$$ with $$2<q<2^{*}_{s}\le r$$ and $$\lambda >0$$ , by combining a truncation argument and a Moser-type iteration.
PubDate: 2017-03-17
DOI: 10.1007/s10231-017-0652-5

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