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.
domain perturbation. boundary value problems for elliptic equations.
AMS Subject Classification (1991)
Secondary: 35J25, 35J65
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Sydney Mathematics and Statistics