Calculus of Variations and Geometric Measure Theory

F. Ebobisse - M. Ponsiglione

A duality approach for variational problems in domains with cracks

created on 13 Dec 2002
modified by ponsiglio on 05 Jan 2005


Published Paper

Inserted: 13 dec 2002
Last Updated: 5 jan 2005

Journal: J. Convex Anal.
Volume: 11
Number: 1
Pages: 17-40
Year: 2004


In this paper we study the asymptotic behaviour of the solutions of some minimization problems for integral functionals with convex integrands, in two-dimensional domains with cracks, under perturbations of the cracks in the Hausdorff metric. In the first part of the paper, we examine conditions for the stability of the minimum problem via duality arguments in convex optimization. In the second part, we study the limit problem in some special cases when there is no stability, using the tool of Gamma-convergence.

Keywords: Gamma-convergence, capacity, Convex optimization, Hausdorff distance