Domain perturbation for elliptic equations subject to Robin boundary conditions

Authors

Dancer E.N. and Daners D.

Status

Research Report 96-30
Date: 22 August 1996

Abstract

We prove domain perturbation theorems for linear and nonlinear elliptic equations under Robin boundary conditions. The theory allows very singular perturbation of domains. In particular, it includes cutting holes, parts degenerating to a set of measure zero such as the dumbbell problem, or wildly oscillating boundaries. In the last case we show that the limiting problem is the Dirichlet problem.

Key phrases

domain perturbation. boundary value problems for elliptic equations.

AMS Subject Classification (1991)

Primary: 35B20
Secondary: 35J25, 35J65

Content

The paper is available in the following forms:

PostScript:: 1996-30.ps.gz (136kB) or 1996-30.ps (436kB)

To minimize network load, please choose the smaller gzipped .gz form if and only if your browser client supports it.

Sydney Mathematics and Statistics