Quasilinear elliptic equations with signed measure

Neil S. Trudinger; Xu-Jia Wang

doi:10.3934/dcds.2009.23.477

Article Contents

2009, Volume 23, Issue 1&2: 477-494. Doi: 10.3934/dcds.2009.23.477

This issue Previous Article On energetic variational approaches in modeling the nematic liquid crystal flows Next Article Stationary solutions to the exterior problems for the Boltzmann equation, I. Existence

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

Received: November 2007

Revised: March 2008

Published: May 2009

Abstract Related Papers Cited by

Abstract

This paper treats quasilinear elliptic equations indivergence form whose inhomogeneous term is a signed measure. Wefirst prove the existence and continuity of generalized solutions tothe Dirichlet problem. The main result of this paper is a weakconvergence result, extending previous work of the authors forsubharmonic functions and non-negative measures. We also prove auniqueness result for uniformly elliptic operators and for operatorsof $p$-Laplacian type.

Keywords:

Mathematics Subject Classification: Primary: 35J60; Secondary: 35D05.

Citation:

Article Metrics

HTML views() PDF downloads(149) Cited by(0)

Quasilinear elliptic equations with signed measure

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

Quasilinear elliptic equations with signed measure

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content