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Discrete and Continuous Dynamical Systems - Series A (DCDS-A)
 

Quasilinear elliptic equations with signed measure

Pages: 477 - 494, Volume 23, Issue 1/2, January/February 2009      doi:10.3934/dcds.2009.23.477

 
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Neil S. Trudinger - Centre for Mathematics and Its Applications, the Australian National University, Canberra, ACT 0200, Australia (email)
Xu-Jia Wang - Centre for Mathematics and Its Applications, Australian National University, Canberra, ACT 0200, Australia (email)

Abstract: 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, weak convergence, existence
Mathematics Subject Classification:  Primary: 35J60; Secondary: 35D05

Received: November 2007;      Revised: March 2008;      Available Online: September 2008.