Perron's Method and Wiener's Theorem for a Nonlocal Equation

TL;DR

This paper investigates the Dirichlet problem for nonlocal fractional p-Laplacian equations, applying Perron's method and establishing Wiener's resolutivity theorem to advance understanding of boundary value problems in nonlocal PDEs.

Contribution

It introduces the application of Perron's method and proves Wiener's theorem for fractional p-Laplacian equations, extending classical potential theory to nonlocal operators.

Findings

Established resolutivity of boundary problems using Wiener's theorem.

Demonstrated the effectiveness of Perron's method for nonlocal fractional equations.

Extended classical potential theory results to fractional p-Laplacian operators.

Abstract

We study the Dirichlet problem for non-homogeneous equations involving the fractional $p$-Laplacian. We apply Perron's method and prove Wiener's resolutivity theorem.