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The Free Boundary Problem in the Optimization of Composite Membranes | | S. Chanillo
; D. Grieser
; K. Kurata
; | | Date: |
15 Dec 1999 | | Subject: | Analysis of PDEs; Optimization and Control MSC-class: 35R35 (Primary), 49Q10, 35B99, 35P30 (Secondary) | math.AP math.OC | | Abstract: | 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 $OmegasubsetR^n$ and numbers $alphageq 0$, $Ain [0,|Omega|]$, find a subset $DsubsetOmega$ 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. | | Source: | arXiv, math.AP/9912117 | | Services: | Forum | Review | PDF | Favorites | |
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