Dirichlet Problems on Varying Domains

Daniel Daners
Journal of Differential Equations 188 (2003), 591-624.
Original available at doi:10.1016/S0022-0396(02)00105-5
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The aim of the paper is to characterise sequences of domains for which solutions to an elliptic equation with Dirichlet boundary conditions converge to a solution of the corresponding problem on a limit domain. Necessary and sufficient conditions are discussed for strong and uniform convergence for the corresponding resolvent operators. Examples are given to illustrate that most results are optimal.

AMS Subject Classification (2000): 35B20 (35B25, 35J25)

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