Regularity of the minimizers in the composite membrane problem in R²

2008/04/07 by Sagun Chanillo, Carlos E. Kenig, Chanillo, Sagun +3
Mathematics · #35R35 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35R35

paper · pdf · doi:10.48550/arxiv.0804.1094

arxiv created 2008/04/07 · arxiv updated 2009/12/01

Abstract

We study the regularity of minimizers to the composite membrane problem in the plane (ie given a domain omega and a positive number A, smaller than the measure of omega, minimize the first Dirichlet eigenvalue for the Schrodinger operator with potential equal to a fixed multiple of the characteristic function of a subset D of omega, with measure A). We show that for minimizers, the boundary of D is analytic.

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