Regularity of the minimizers in the composite membrane problem in R^2
Kenig, Carlos E.
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.
Mathematics - Analysis of PDEs, 35R35