Optimal solvability for the fractional p-Laplacian with Dirichlet conditions
Analysis of PDEs
2023-12-08 v3
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.
Keywords
Cite
@article{arxiv.2206.08685,
title = {Optimal solvability for the fractional p-Laplacian with Dirichlet conditions},
author = {Antonio Iannizzotto and Dimitri Mugnai},
journal= {arXiv preprint arXiv:2206.08685},
year = {2023}
}
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17 pages