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

2020/10/22 by M. Allen, Allen, Mark, Dennis Kriventsov +3 · 2 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Differential Equations and Boundary Problems #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2010.11854

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.

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