Kato's inequalities up to the boundary for a quasilinear elliptic operator

TL;DR

This paper extends Kato's inequalities involving measures to the boundary for the p-Laplace operator in smooth bounded domains, providing new boundary estimates under specific conditions.

Contribution

It establishes boundary Kato's inequalities for the p-Laplace operator involving measures, advancing the understanding of boundary behavior in nonlinear elliptic PDEs.

Findings

Kato's inequalities are valid up to the boundary for the p-Laplace operator.

Boundary estimates are derived under suitable assumptions.

The results apply to measures in bounded smooth domains.

Abstract

In a bounded smooth domain of Rn, we shall establish Kato's inequalities involving measures for p-Laplace operator up to the boundary under suitable assumptions. Keywords: Kato's inequality, $p$-Laplace operator