Hopf's lemmas and boundary behaviour of solutions to the fractional Laplacian in Orlicz-Sobolev spaces

2024/11/20 by Ochoa, Pablo, Salort, Ariel
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2411.13498

Abstract

In this article we study different extensions of the celebrated Hopf's boundary lemma within the context of a family of nonlocal, nonlinear and nonstandard growth operators. More precisely, we examine the behavior of solutions of the fractional a-Laplacian operator near the boundary of a domain satisfying the interior ball condition. Our approach addresses problems involving both constant-sign and sign-changing potentials.

Related

• Hopf's lemmas and boundary point results for the fractional p-Laplacian
• Neumann and Robin type boundary conditions in Fractional Orlicz-Sobolev spaces
• A fractional Hopf Lemma for sign-changing solutions
• Boundary behavior of solutions to fractional p-Laplacian equation
• A Hopf's Lemma and the Boundary Regularity for the Fractional P-Laplacian