JournalsaihpcVol. 36, No. 2pp. 455–474

Existence of strong minimizers for the Griffith static fracture model in dimension two

  • Sergio Conti

    Institut für Angewandte Mathematik, Universität Bonn, 53115 Bonn, Germany
  • Matteo Focardi

    DiMaI, Università di Firenze, 50134 Firenze, Italy
  • Flaviana Iurlano

    Laboratoire Jacques-Louis Lions, Université Paris 6, 75005 Paris, France
Existence of strong minimizers for the Griffith static fracture model in dimension two cover
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Abstract

We consider the Griffith fracture model in two spatial dimensions, and prove existence of strong minimizers, with closed jump set and continuously differentiable deformation fields. One key ingredient, which is the object of the present paper, is a generalization to the vectorial situation of the decay estimate by De Giorgi, Carriero, and Leaci. This is based on replacing the coarea formula by a method to approximate SBDpSBD^{p} functions with small jump set by Sobolev functions, and is restricted to two dimensions. The other two ingredients will appear in companion papers and consist respectively in regularity results for vectorial elliptic problems of the elasticity type and in a method to approximate in energy GSBDpGSBD^{p} functions by SBVpSBV^{p} ones.

Cite this article

Sergio Conti, Matteo Focardi, Flaviana Iurlano, Existence of strong minimizers for the Griffith static fracture model in dimension two. Ann. Inst. H. Poincaré Anal. Non Linéaire 36 (2019), no. 2, pp. 455–474

DOI 10.1016/J.ANIHPC.2018.06.003