A Wiener estimate for relaxed Dirichlet problems in dimension $N\geq 2$

Abstract

We prove a Wiener energy estimate for relaxed Dirichlet problems $Lu + μu =ν$ in $Ω$, with $L$ an uniformly elliptic operator with bounded coefficients, $μ$ a measure of ${\cal M}_0(Ω)$, $ν$ a Kato measure and $Ω$ a bounded open set of ${\bf R}^N$, $N \geq 2$. Choosing a particular $μ$, we obtain an energy estimate also for classical variational Dirichlet problems.