Article ID Journal Published Year Pages File Type
4604487 Annales de l'Institut Henri Poincare (C) Non Linear Analysis 2009 15 Pages PDF
Abstract

We consider the well-known following shape optimization problem:λ1(Ω∗)=min|Ω|=aΩ⊂Dλ1(Ω), where λ1λ1 denotes the first eigenvalue of the Laplace operator with homogeneous Dirichlet boundary condition, and D is an open bounded set (a box). It is well-known that the solution of this problem is the ball of volume a if such a ball exists in the box D (Faber–Krahn's theorem).In this paper, we prove regularity properties of the boundary of the optimal shapes Ω∗Ω∗ in any case and in any dimension. Full regularity is obtained in dimension 2.

Related Topics
Physical Sciences and Engineering Mathematics Analysis
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