The Inhomogeneous Boundary Harnack Principle for Fully Nonlinear and p-Laplace equations

TL;DR

This paper establishes a boundary Harnack principle for fully nonlinear, p-Laplace, and Laplace equations in specific domains, introducing a novel systematic approach applicable to various equations and geometries.

Contribution

It presents a new method for proving boundary Harnack principles applicable to a broad class of nonlinear and linear equations in Lipschitz and NTA domains.

Findings

Boundary Harnack principle proven for fully nonlinear equations.

Extension to p-Laplace and Laplace equations in specific domains.

Introduction of a systematic approach for similar boundary estimates.

Abstract

We prove a boundary Harnack principle in Lipschitz domains with small constant for fully nonlinear and $p$-Laplace type equations with a right hand side, as well as for the Laplace equation on nontangentially accessible domains under extra conditions. The approach is completely new and gives a systematic approach for proving similar results for a variety of equations and geometries.