Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

François Ebobisse

Dept. of Mathematics, University of Cape Town, Rondebosch 7700, South Africa

ebobisse@maths.uct.ac.za

Marcello Ponsiglione

S.I.S.S.A., Via Beirut 2-4, 34014 Trieste, Italy

ponsigli@sissa.it

Keywords

  • capacity
  • convex optimization
  • Gamma-convergence
  • Hausdorff distance
  • integral functional

Mathematics Subject Classification

31A15, 46N10, 49M29, 49J45

Suggested citation

F. Ebobisse, M. Ponsiglione. “A Duality Approach for Variational Problems in Domains with Cracks.” Journal of Convex Analysis 11 (2004), No. 1, 17–40.

Copyright Heldermann Verlag 2004