Remarks on the uniqueness of comparable renormalized solutions of elliptic equations with measure data

TL;DR

This paper investigates the uniqueness of comparable renormalized solutions for nonlinear elliptic equations with measure data, providing partial results under specific conditions.

Contribution

It offers a new partial uniqueness result for comparable renormalized solutions of elliptic equations with measure data, advancing understanding in this area.

Findings

Partial uniqueness result established for comparable renormalized solutions.

Conditions identified under which solutions are unique.

Enhances theoretical understanding of elliptic equations with measure data.

Abstract

We give a partial uniqueness result concerning comparable renormalized solutions of the nonlinear elliptic problem $-\diw(\aop(x,Du))=\mu$ in $\Omega$, $u=0$ on $\partial\Omega$, where $\mu$ is a Radon measure with bounded variation on $\Omega$.