On a variational principle for shape optimization and elliptic free boundary problems

A variational principle for several free boundary value problems using a relaxation approach is presented. The relaxed Energy functional is concave and it is defined on a convex set, so that the minimizing points are characteristic functions of sets. As a consequence of the first order optimality co...

Full description

Main Author: González De Paz, Raúl B.
Format: Artículo
Language: Español
Published: 2015
Online Access: http://revistas.ucr.ac.cr/index.php/matematica/article/view/169
http://hdl.handle.net/10669/12805
Summary: A variational principle for several free boundary value problems using a relaxation approach is presented. The relaxed Energy functional is concave and it is defined on a convex set, so that the minimizing points are characteristic functions of sets. As a consequence of the first order optimality conditions, it is shown that the corresponding sets are domains bounded by free boundaries, so that the equivalence of the solution of the relaxed problem with the solution of several free boundary value problem is proved.Keywords: Calculus of variations, optimization, free boundary problems.