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Juan F. Spedaletti

Publications and source records attributed to Juan F. Spedaletti.

6 recordsLinked to original sources
arXiv2026

An eigenvalue problem for a nonlocal quasilinear anisotropic equation in fractional Orlicz Sobolev spaces without the $Δ_2$--condition

In this paper we analyze an eigenvalue problem associated to fractional operators of the form \[ L_a^s u(x)=2 \text{p.v.}\int_{\mathbb{R}^n}a(x,y,D^su(x,y))\,\frac{dy}{|x-y|^{n+s}},\] which represents a generalization model for nonlocal, nonstandard growth diffusion problems. We study this problem in the context of the fractional Orlicz Sobolev spaces without assuming the so-called $Δ_2$--condition on the Young functions involved. We show existence of a sequence of eigenpairs $(u_k,λ_k)\to (0,+\infty)$.

math.AP↗
arXiv2024

Ljusternik-Schnirelmann eigenvalues for the fractional $m-$Laplacian without the $Δ_2$ condition

In this work we analyze the eigenvalue problem associated to the fractional $m-$Laplacian, defined as $$ (-Δ_m)^s u(x):=2\text{p.v.}\int_{{\mathbb R}^n} m\left(\frac{|u(x)-u(y)|}{|x-y|^s}\right)\frac{(u(x)-u(y))}{|u(x)-u(y)|}\frac{dy}{|x-y|^{n+s}}, $$ This operator serves as a model for nonlocal, nonstandard growth diffusion problems. In contrast to previous analyses, we explore the eigenvalue problem without presuming the $Δ_2$ condition on $M$ -- the primitive function of $m$. Our results show the existence of a sequence of eigenvalues $λ_k\to\infty$. This research contributes to advancing our understanding of nonlocal diffusion models, specifically those characterized by the fractional $m-$Laplacian, by relaxing the constraints imposed by the $Δ_2$ condition.

math.AP↗
arXiv2019

Gamma convergence and asymptotic behavior for eigenvalues of nonlocal problems

In this paper we analyze the asymptotic behavior of several fractional eigenvalue problems by means of Gamma-convergence methods. This method allows us to treat different eigenvalue problems under a unified framework. We are able to recover some known results for the behavior of the eigenvalues of the $p-$fractional laplacian when the fractional parameter $s$ goes to 1, and to extend some known results for the behavior of the same eigenvalue problem when $p$ goes to $\infty$. Finally we analyze other eigenvalue problems not previously covered in the literature.

math.AP↗
arXiv2017

Optimal design problems for the first $p-$fractional eigenvalue with mixed boundary conditions

In this paper we study an optimal shape design problem for the first eigenvalue of the fractional $p-$laplacian with mixed boundary conditions. The optimization variable is the set where the Dirichlet condition is imposed (that is restricted to have measure equal than a prescribed quantity, $α$). We show existence of an optimal design and analyze the asymptotic behavior when the fractional parameter $s\uparrow 1$ obtaining asymptotic bounds that are independent of $α$.

math.AP↗