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

Abstract

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