Domain with a crack

In this subsection we prove an existence theorem for the elastoplastic problem in the case where the domain has a nonsmooth boundary. 

let c i be a bounded domain with a smooth boundary T and Tc C H be a smooth orientable two-dimensional surface with a regular boundary. We assume that Tc can be extended in such a way that the domain fl is divided into two parts with Lipschitz boundaries. The surface Tc can be described parametrically 

All notations fit those used in the preceding subsection. As we see, in this case the boundary of the domain consists of the parts F, F+, Fj, where F correspond to the positive and negative directions of the normal i/, respectively. Introduce the space 

to simplify the formulae we assume Cijki =. Recall that the set 

The general scheme of reasoning coincides with that used in the proof of Theorem 5.3 and our attention now focuses on details related to the nonsmoothness of the boundary. 

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