Eigenvalues for a nonlocal pseudo p-Laplacian

In this paper we study the eigenvalue problems for a nonlocal operator of order s that is analogous to the local pseudo p-Laplacian. We show that there is a sequence of eigenvalues λn→ ∞and that the first one is positive, simple, isolated and has a positive and bounded associated eigenfunction. For the first eigenvalue we also analyze the limits as p → ∞ (obtaining a limit nonlocal eigenvalue problem analogous to the pseudo infinity Laplacian) and as s → 1- (obtaining the first eigenvalue for a local operator of p-Laplacian type). To perform this study we have to introduce anisotropic fractional Sobolev spaces and prove some of their properties.Fil: del Pezzo, Leandro Martin. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Rossi, Julio Daniel. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin