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Quasilinear elliptic equations with signed measure data

Wang, Xu-Jia; Trudinger, Neil


This paper treats quasilinear elliptic equations in divergence form whose inhomogeneous term is a signed measure. We first prove the existence and continuity of generalized solutions to the Dirichlet problem. The main result of this paper is a weak convergence result, extending previous work of the authors for subharmonic functions and non-negative measures. We also prove a uniqueness result for uniformly elliptic operators and for operators of p-Laplacian type.

CollectionsANU Research Publications
Date published: 2009-01
Type: Journal article
Source: Discrete and Continuous Dynamical Systems - Series A
DOI: 10.3934/dcds.2009.23.477


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