article

Title: On a minimization problem with a mass constraint in dimension two

Authors: Itai Shafrir and Nelly Andre

Issue: Volume 63 (2014), Issue 2, 419-445

Abstract:

$We continue our study that was begun in [N. Andr\'e and I. Shafrir, \textit{On a minimization problem with a mass constraint involving a potential vanishing on two curves}, Israel J. Math. \textbf{186} (2011), 97--124.] of a singular perturbation-type minimization problem with a mass constraint, involving a potential vanishing on two curves in the plane. In the case of a two-dimensional nonconvex domain (and under some additional assumptions), we are able to prove a convergence result for the minimizers, and characterize the limit as a solution of a mixed Dirichlet-Neumann boundary condition problem with a mass constraint.$