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

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.