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

摘要

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) curved right arrow L-q(partial derivative Omega) for functions that vanish in a subset of Omega. This problem is also related to a minimization problem for Steklov eigenvalues.