Regularity of the minimizers in the composite membrane problem in R^2

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Chanillo, Sagun
Kenig, Carlos E.
TO, Tung
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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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Mathematics - Analysis of PDEs, 35R35
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