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

Dal Maso, Gianni; Mosco, Umberto

Arch. Ration. Mech. Anal. 95, 345-387 (1986).

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

MSC:

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)

Keywords:

relaxed Dirichlet problem; Wiener criteria; uniformly elliptic; measurable coefficients; local weak solution

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