Cauchy integrals for the p-Laplace equation in planar Lipschitz domains

TL;DR

This paper develops a method using Cauchy integrals to construct solutions for p-Laplace equations in planar Lipschitz domains, enabling prescribed boundary data in fractional Sobolev spaces.

Contribution

It introduces a novel Cauchy integral representation formula for p-Laplace equations in Lipschitz domains, expanding solution construction techniques.

Findings

Constructed solutions with prescribed boundary data in fractional Sobolev spaces.

Established a Cauchy integral representation formula for p-Laplace equations.

Extended analytical tools for nonlinear PDEs in Lipschitz domains.

Abstract

We construct solutions to p-Laplace type equations in unbounded Lipschitz domains in the plane with prescribed boundary data in appropriate fractional Sobolev spaces. Our approach builds on a Cauchy integral representation formula for solutions.