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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

Authors:C. Bargetz; E. A. Nigsch; N. Ortner Abstract: Abstract We apply L. Schwartz’ theory of vector-valued distributions in order to simplify, unify and generalize statements about convolvability of distributions, their regularization properties and topological properties of sets of distributions. The proofs rely on propositions on the multiplication of vector-valued distributions and on the characterization of the spaces \(\mathcal {O}_{M}(E,F)\) and \(\mathcal {O}_{C}'(E,F)\) of multipliers and convolutors for distribution spaces E and F. PubDate: 2017-04-26 DOI: 10.1007/s10231-017-0662-3

Authors:Calin Iulian Martin Abstract: Abstract We show that gravity wave trains governed by the equatorial f-plane approximation propagate at the free surface of a rotational water flow of constant vorticity vector \((\Omega _1, \Omega _2, \Omega _3)\) over a flat bed only if the flow is two-dimensional. Owing to the presence of Coriolis effects, our result is also true even if the vorticity vector vanishes. This represents a striking difference when compared with the cases without geophysical effects discussed in Constantin (Europhys Lett 86:29001, 2009, Eur J Mech 30:12–16; 2011) and Martin (J Math Fluid Mech 2016. doi:10.1007/s00021-016-0306-1), where the conclusion about the two-dimensionality of the flow was possible under the assumption of constant nonvanishing vorticity vector. Another upshot is that the only nonzero component of the vorticity that may not vanish is \(\Omega _2\) , that is, the one pointing in the horizontal direction orthogonal to the direction of wave propagation. PubDate: 2017-04-22 DOI: 10.1007/s10231-017-0663-2

Authors:Jie Fei; Ling He Abstract: Abstract In this paper we determine all homogeneous minimal immersions of 2-spheres in quaternionic projective spaces \({\mathbb {H}}P^n\) . PubDate: 2017-04-22 DOI: 10.1007/s10231-017-0661-4

Authors:Flavia Giannetti; Antonia Passarelli di Napoli; Atsushi Tachikawa Abstract: Abstract We prove the partial Hölder continuity of the local minimizers of non-autonomous integral functionals of the type $$\begin{aligned} \int _\varOmega \varPhi \left( \big ( A^{\alpha \beta }_{ij}(x,u) D_iu^\alpha D_ju^\beta \big )^{1/2}\right) \mathrm{d}x, \end{aligned}$$ where \(\varPhi \) is an Orlicz function satisfying both the \(\varDelta _2\) and \(\nabla _2\) conditions and the function \(A(x,s) = \big (A^{\alpha \beta }_{ij}(x,s)\big )\) is uniformly elliptic, bounded and continuous. Assuming in addition that the function \(A(x,s) = \big (A^{\alpha \beta }_{ij}(x,s)\big )\) is Hölder continuous, we prove the partial Hölder continuity also of the gradient of the local minimizers. PubDate: 2017-04-13 DOI: 10.1007/s10231-017-0658-z

Authors:Sharief Deshmukh Abstract: Abstract It is well known that the Euclidean space \( (R^{n},\left\langle ,\right\rangle )\) , the n-sphere \(S^{n}(c)\) of constant curvature c are examples of spaces admitting many conformal vector fields, and therefore conformal vector fields are used in obtaining characterizations of these spaces. In this paper, we use nontrivial conformal vector fields on a compact and connected Riemannian manifold to characterize the sphere \(S^{n}(c)\) . Also, we use a nontrivial conformal vector field on a complete and connected Riemannian manifold and find characterizations for a Euclidean space \((R^{n},\left\langle ,\right\rangle )\) and the sphere \(S^{n}(c)\) . PubDate: 2017-04-06 DOI: 10.1007/s10231-017-0657-0