N-dimensional shape optimization under capacitary constraint

[摘要] New capacitary constraints are introduced in the study of the solution of a Dirichlet problem in terms of the domain variation. Using the Hausdorff topology in the space of open sets we prove the strong continuity of solutions under some capacitary constraints on geometrical domains. We introduce simpler grometrical constraints, the flat cone condition, under which the continuity result still holds. We deduce the existence of extremal points for continuous shape functionals on these families of domains which turns out to be compact. (C) 1995 Academic Press, Inc.

[发布日期] 1995-12-10