Regularity of the free boundary in an optimization problem related to the best Sobolev trace constant.

JULIAN FERNANDEZ BONDER; ROSSI, JULIO DANIEL; WOLANSKI, NOEMI IRENE

SIAM JOURNAL ON CONTROL AND OPTIMIZATION

SIAM PUBLICATIONS

Año: 2005 p. 1614 - 1635

0363-0129

In this paper we study the regularity properties of a free boundary problem arising in the optimization of the best Sobolev trace constant in the immersion $H^1(Omega)subset L^q(partial Omega)$ for functions that vanish in a subset of $Omega$. This problem is also related to a minimization problem for Steklov eigenvalues.H^1(Omega)subset L^q(partial Omega)$ for functions that vanish in a subset of $Omega$. This problem is also related to a minimization problem for Steklov eigenvalues.