Persona: Ortega García, Alejandro
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alejandro.ortega@mat.uned.es
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0000-0003-1902-4275
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Ortega García
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Alejandro
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Publicación On the Robin function for the fractional Laplacian on symmetric domains(Springer Nature, 2024-01-04) Ortega García, AlejandroIn 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.Publicación New Functional Inequalities with Applications to the Arctan-Fast Diffusion Equation(Springer, 2025-04-15) Granero Belinchón, Rafael; Magliocca, Martina; Ortega García, AlejandroPublicación Fractional critical systems with mixed boundary conditions(Springer, 2026-02-20) Kumar, Rohit; Ortega García, AlejandroIn this paper, we analyze the existence of solution for a fractional elliptic system coupled by critical nonlinearities and endowed with mixed Dirichlet-Neumann boundary conditions. By means of variational methods and an orthogonalization-like process in the corresponding Sobolev space, we establish the existence of at least one weak solution.Publicación Pervasiveness of the p-Laplace operator under localization of fractional g-Laplace operators(Biemdas Academic Publishers, 2025-06-01) Ortega García, AlejandroIn 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.Publicación Fractional Schrödinger systems coupled by Hardy-Sobolev critical terms(Khayyam Publishing, Inc., 2025-08-27) Ortega García, AlejandroIn this work, we analyze a class of nonlinear fractional elliptic systems involving Hardy-type potentials and coupled by critical Hardy-Sobolev-type nonlinearities in RN. Due to the lack of compactness at the critical exponent the variational approach requires a careful analysis of the Palais-Smale sequences. In order to overcome this loss of compactness, by means of a concentration– compactness argument the compactness of PS sequences is derived. This, combined with a energy characterization of the semi-trivial solutions, allow us to conclude the existence of positive ground and bound state solutions in terms of coupling parameter ν>0 and the involved exponents α,β.Publicación Positive solutions for a weighted critical problem with mixed boundary conditions(American Institute of Mathematical Sciences, 2025-12-01) Ortega García, Alejandro; Vilasi, Luca; Wang, YoujunWe analyze the existence and multiplicity of positive solutions to a nonlocal elliptic problem involving the spectral fractional Laplacian endowed with homogeneous mixed Dirichlet-Neumann boundary conditions and weighted critical nonlinearities. By means of variational methods and the Nehari manifold approach, we deduce the existence of multiple positive solutions under some assumptions on the behavior of the weight function around its maximum points. In this way, we extend and improve the results in [19], dealing with the Dirichlet problem for the classical Laplacian, to the nonlocal setting with mixed boundary conditions.Publicación Subcritical nonlocal problems with mixed boundary conditions(World Scientific Publishing, 2014-01) Molica Bisci, Giovanni; Ortega García, Alejandro; Luca VilasiBy 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.Publicación Nonlinear elliptic systems involving Hardy-Sobolev Criticalities(Springer, 2023-08-23) López-Soriano, Rafael; Ortega García, AlejandroThis 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.