Regularity of the minimizers in the composite membrane problem in R^2 - Mathematics > Analysis of PDEsReport as inadecuate




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Abstract: We study the regularity of minimizers to the composite membrane problem inthe plane ie given a domain omega and a positive number A, smaller than themeasure of omega, minimize the first Dirichlet eigenvalue for the Schrodingeroperator with potential equal to a fixed multiple of the characteristicfunction of a subset D of omega, with measure A. We show that for minimizers,the boundary of D is analytic.



Author: Sagun Chanillo, Carlos E.Kenig, Tung TO

Source: https://arxiv.org/







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