IJPAM: Volume 40, No. 4 (2007)

A VARIATIONAL APPROXIMATION INHERITING
A NON-DEGENERACY PROPERTY

Yoshihiko Yamaura
Department of Mathematics
College of Humanities and Sciences
Nihon University
3-25-40, Sakurajosui, Setagaya-ku, Tokyo, 156-8550, JAPAN
e-mail: yamaura@math.chs.nihon-u.ac.jp


Abstract.We investigate an approximation to a variational functional with a singular term whose minimizers may have a free boundary. The approximation is considered in the sense of $\Gamma$-convergence, that is, a variational convergence. Our aim of this paper is to establish a criterion for the location of the free boundary in terms of the approximation. As a corollary, approximated minimizers are proved to inherit a non-degeneracy property in some weak sense. These results depend on a certain device of the choice of approximation of the singular term.

Received: September 7, 2007

AMS Subject Classification: 49Q20, 37E35

Key Words and Phrases: $\Gamma$-convergence, Radon measures, non-degeneracy

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 40
Issue: 4