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Existence of minimizers for the d stationary Griffith fracture model
We consider the variational formulation of the Griffith fracture model in two
spatial dimensions and prove existence of strong minimizers, that is
deformation fields which are continuously differentiable outside a closed jump
set and which minimize the relevant energy. To this aim, we show that
minimizers of the weak formulation of the problem, set in the function space
and for which existence is well-known, are actually strong minimizers
following the approach developed by De Giorgi, Carriero, and Leaci in the
corresponding scalar setting of the Mumford-Shah problem
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