Wiener criteria and energy decay for relaxed Dirichlet problems (Q1096785)

The main purpose of the work is to develop a pointwise analysis for equations of the form \(Lu+\mu u=\nu\) in \(\Omega\in {\mathbb{R}}^ n \)where L is a uniformly elliptic operator with bounded Lebesgue-measurable coefficients, \(\nu\) is some given Radon measure in \({\mathbb{R}}^ n \)and \(\mu\) is a given Borel measure which is admissable for this problem in a certain natural sense. The authors consider a local weak solution in \(H\) \(1_{loc}(\Omega)\cap L\) \(2_{loc}(\Omega,\mu)\) and study it at an arbitrary point \(x_ 0\in \Omega\).