Domain perturbation for elliptic equations subject to Robin boundary conditions


Dancer E.N. and Daners D.


Research Report 96-30
Date: 22 August 1996


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


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