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

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