Domain Perturbation for Elliptic Equations Subject to Robin Boundary Conditions - Dancer, E.N.; Daners, D. (Journal of Differential Equations, 1997)
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.