Optimal solvability for the fractional p-Laplacian with Dirichlet conditions

2022/06/17 by Antonio Iannizzotto, Iannizzotto, Antonio, Dimitri Mugnai +1
Computer Science · Mathematics · #34A15 #35P30 #35R11 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2206.08685

openalex publication_date 2022/06/17 · openalex created_date 2022/06/22 · openalex updated_date 2026/07/28

Abstract

We study a nonlinear, nonlocal Dirichlet problem driven by the fractional p-Laplacian, involving a (p-1)-sublinear reaction. By means of a weak comparison principle we prove uniqueness of the solution. Also, comparing the problem to 'asymptotic' weighted eigenvalue problems for the same operator, we prove a necessary and sufficient condition for the existence of a solution. Our work extends classical results due to Brezis-Oswald and Diaz-Saa to the quasilinear nonlocal framework.

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