Quasilinear elliptic equations with signed measure
Neil S. Trudinger - Centre for Mathematics and Its Applications, the 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
Received: November 2007; Revised: March 2008; Published: September 2008.
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