Article
MSC:
35J05,
35J20,
35J25,
35Qxx,
49-xx | MR 3034822 | Zbl 1274.35062 | DOI: 10.1007/s10492-013-0010-x
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Keywords:
shape optimization; Bernoulli; free boundary problem; exterior Bernoulli problem; optimal solution; state problem; continuity of the state problem; uniform tubular neighbourhood; diffeomorphism; uniform trace theorem; uniform Poincaré inequality
shape optimization; Bernoulli; free boundary problem; exterior Bernoulli problem; optimal solution; state problem; continuity of the state problem; uniform tubular neighbourhood; diffeomorphism; uniform trace theorem; uniform Poincaré inequality
Summary:
We are interested in an optimal shape design formulation for a class of free boundary problems of Bernoulli type. We show the existence of the optimal solution of this problem by proving continuity of the solution of the state problem with respect to the domain. The main tools in establishing such a continuity are a result concerning uniform continuity of the trace operator with respect to the domain and a recent result on the uniform Poincaré inequality for variable domains.
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