Mathematics – Analysis of PDEs
Scientific paper
1999-12-15
Mathematics
Analysis of PDEs
20 pages
Scientific paper
This is a continuation of the paper 'Symmetry breaking and other phenomena in the optimization of eigenvalues for composite membranes' by S. Chanillo, D. Grieser, M. Imai, K. Kurata, and I. Ohnishi. Again, we consider the following eigenvalue optimization problem: Given a bounded domain $\Omega\subset\R^n$ and numbers $\alpha\geq 0$, $A\in [0,|\Omega|]$, find a subset $D\subset\Omega$ of area $A$ for which the first Dirichlet eigenvalue of the operator $-\Delta + \alpha \chi_D$ is as small as possible. In this paper we focus on the study of the free boundary of optimal solutions on general domains.
Chanillo Sagun
Grieser Daniel
Kurata Koji
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