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

摘要

We study the regularity of the minimizers to the problem: lambda(alpha, A) = inf(u is an element of H0)((Omega), parallel to u parallel to 2 = 1, |D| = A)(1) integral(Omega)|Du|(2) + alpha integral(D)u(2). We prove that in the physical case a c} is analytic where c is the constant such that D = {u < c} (up to a zero measure set). (C) 2008 Elsevier Inc. All rights reserved.