Mathematics – Analysis of PDEs
Scientific paper
2008-04-07
Mathematics
Analysis of PDEs
Scientific paper
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.
Chanillo Sagun
Kenig Carlos E.
To Tung
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