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January & February  2009, 23(1&2): 477-494. doi: 10.3934/dcds.2009.23.477

Quasilinear elliptic equations with signed measure

Neil S. Trudinger 1, and  Xu-Jia Wang 2,

1. 

Centre for Mathematics and Its Applications, the Australian National University, Canberra, ACT 0200, Australia
2. 

Centre for Mathematics and Its Applications, Australian National University, Canberra, ACT 0200, Australia

Received  November 2007 Revised  March 2008 Published  September 2008

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.
Keywords: Elliptic equation, existence, weak convergence.
Mathematics Subject Classification: Primary: 35J60; Secondary: 35D05.
Citation: Neil S. Trudinger, Xu-Jia Wang. Quasilinear elliptic equations with signed measure. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 477-494. doi: 10.3934/dcds.2009.23.477
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