A duality approach for variational problems in domains with cracks

Details A duality approach for variational problems in domains with cracks A duality approach for variational problems in domains with cracks

2002-12-13

arxiv.org/abs/math/0212188v1

Mathematics

Functional Analysis

25 pages, 5 figures

Scientific paper

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.

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