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Ortega García, Alejandro

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0000-0003-1902-4275
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Ortega García
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Alejandro
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2014 - 201912020 - 20253
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Mostrando 1 - 4 de 4
  • Miniatura
    Publicación
    Pervasiveness of the p-Laplace operator under localization of fractional g-Laplace operators
    (Biemdas Academic Publishers, 2025-06-01) Ortega García, Alejandro
    In this paper, we analyze the behavior of the truncated functionals as (Formula presented) for δ → 0+, where G is an Orlicz function which is assumed to be regularly varying at 0. A prototype of such function is given by G(t) = tp(1+ |log(t)|) with p ≥ 2. These kinds of functionals arise naturally in peridynamics, where long-range interactions are neglected and only those that exerted at distance smaller than δ > 0 are taken into account, i.e., the horizon δ > 0 represents the range of interactions or nonlocality. This paper is inspired by the celebrated result by Bourgain, Brezis and Mironescu, who analyzed the limit s → 1− with G(t) = tp. In particular, we prove that, under appropriate conditions, (Formula presented) for p = index(G) and an explicit constant KN,p > 0. Moreover, the converse is also true if the above localization limit exist as δ → 0+, and the Orlicz function G is a regularly varying function with index(G) = p.
  • Miniatura
    Publicación
    On the Robin function for the fractional Laplacian on symmetric domains
    (Springer Nature, 2024-01-04) Ortega García, Alejandro
    In this work we prove, under symmetry and convexity assumptions on the domain Ω, the non-degeneracy at zero of the Hessian matrix of the Robin function for the spectral fractional Laplacian. This work extends to the fractional setting the results of M. Grossi concerning the classical Laplace operator.
  • Miniatura
    Publicación
    Nonlinear elliptic systems involving Hardy-Sobolev Criticalities
    (Springer, 2023-08-23) López-Soriano, Rafael; Ortega García, Alejandro
    This paper is focused on the solvability of a family of nonlinear elliptic systems defined in RN . Such equations contain Hardy potentials and Hardy–Sobolev criticalities coupled by a possible critical Hardy–Sobolev term. That problem arises as a generalization of Gross–Pitaevskii and Bose–Einstein type systems. By means of variational techniques, we shall find ground and bound states in terms of the coupling parameter ν and the order of the different parameters and exponents. In particular, for a wide range of parameters we find solutions as minimizers or Mountain–Pass critical points of the energy functional on the underlying Nehari manifold.
  • Miniatura
    Publicación
    Subcritical nonlocal problems with mixed boundary conditions
    (World Scientific Publishing, 2014-01) Molica Bisci, Giovanni; Ortega García, Alejandro; Luca Vilasi
    By using linking and ∇-theorems in this paper we prove the existence of multiple solutions for the following nonlocal problem with mixed Dirichlet–Neumann boundary data, (Formular Presented) where (−Δ)s, s ∈ (1/2, 1), is the spectral fractional Laplacian operator, Ω ⊂ RN, N > 2s, is a smooth bounded domain, λ > 0 is a real parameter, ν is the outward normal to ∂Ω, ΣD, ΣN are smooth (N − 1)-dimensional submanifolds of ∂Ω such that ΣD ∪ ΣN = ∂Ω, ΣD ∩ ΣN = ∅ and ΣD ∩ ΣN = Γ is a smooth (N − 2)-dimensional submanifold of ∂Ω.