Calculus of Variations and Geometric Measure Theory

A. Garroni

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

created by garroni on 18 Sep 2020


Published Paper

Inserted: 18 sep 2020
Last Updated: 18 sep 2020

Journal: Differential and Integral Equations
Volume: 4
Number: 3
Pages: 373-407
Year: 1993

ArXiv: funct-an/9303003 PDF


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