A Wiener estimate for relaxed Dirichlet problems in dimension $N\geq 2$
Adriana Garroni · Differential and Integral Equations · 1995
We prove a Wiener energy estimate for relaxed Dirichlet problems $Lu + \mu u = u$ in $\Omega$, with $L$ a uniformly elliptic operator with bounded coefficients, $\mu$ a measure of $\mathcal {M}_0(\Omega)$, $ u$ a Kato measure and $\Omega$ a bounded open set of $\mathbb{R}^N$, $N \geq 2$. Choosing a particular $\mu$, we obtain an energy estimate also for classical variational Dirichlet problems.