Wiener criteria and energy decay for relaxed Dirichlet problems. (English) Zbl 0634.35033

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 \(x_ 0\in \Omega\).
Reviewer: G.Dzuik


35J70 Degenerate elliptic equations
35J20 Variational methods for second-order elliptic equations
35B40 Asymptotic behavior of solutions to PDEs
35A07 Local existence and uniqueness theorems (PDE) (MSC2000)
35B65 Smoothness and regularity of solutions to PDEs
35D10 Regularity of generalized solutions of PDE (MSC2000)
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