Regularity of the minimizers in the composite membrane problem in R^2
Analysis of PDEs
2008-04-08 v1
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.
Keywords
Cite
@article{arxiv.0804.1094,
title = {Regularity of the minimizers in the composite membrane problem in R^2},
author = {Sagun Chanillo and Carlos E. Kenig and Tung TO},
journal= {arXiv preprint arXiv:0804.1094},
year = {2008}
}