Existence for doubly nonlinear fractional $p$-Laplacian equations

TL;DR

This paper establishes the existence of weak solutions for a broad class of doubly nonlinear fractional p-Laplacian equations, covering various nonlinearity regimes and diffusion types, using a weak convergence approach.

Contribution

It introduces a novel proof method employing weak convergence for doubly nonlinear fractional p-Laplacian equations, encompassing diverse nonlinearity and diffusion cases.

Findings

Proved existence of weak solutions for general doubly nonlinear fractional p-Laplacian equations.

Applicable to Sobolev subcritical, critical, and supercritical cases.

Handles slow and fast diffusion regimes.

Abstract

In this paper we prove the existence of a weak solution to a doubly nonlinear parabolic fractional $p$-Laplacian equation, which has general doubly non-linearlity including not only the Sobolev subcritical/critical/supercritical cases but also the slow/fast diffusion ones. Our proof reveals the weak convergence method for the doubly nonlinear fractional $p$-Laplace operator.