1999/12/15 by S. Chanillo, Sagun Chanillo, D. Grieser +6
Engineering · Mathematics · #35B99 #35P30 (Secondary) #35R35 (Primary) #49Q10 #Analysis of PDEs (math.AP) #FOS: Mathematics #Optimization and Control (math.OC) #Structural Analysis and Optimization #math.AP #math.OC #msc:35B99 #msc:35P30 #msc:35R35 #msc:49Q10
paper · pdf · doi:10.48550/arxiv.math/9912117
20 pages
arxiv created 1999/12/15 · openalex publication_date 1999/12/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 Ω⊂\Rn and numbers α≥ 0, A∈ [0,|Ω|], find a subset D⊂Ω of area A for which the first Dirichlet eigenvalue of the operator -Δ+ αχD is as small as possible. In this paper we focus on the study of the free boundary of optimal solutions on general domains.