Domain with the crack

In this subsection we prove the solvability of the elastoplastic problem for a plate having a nonsmooth boundary. A solution of the problem will satisfy all boundary conditions both at the exterior boundary and at the crack faces. 

Let c be a bounded domain with a smooth boundary F, and Fc C be a smooth curve without selfintersections. Assume that Fc contains 

All notations fit those in the previous subsection. Some arguments are required to explain in which sense boundary conditions (5.215) hold. This will be done later on. Note that conditions (5.215) will be contained in an integral identity. 

Consider the Sobolev space IFf (Dc) of functions whose derivatives up to the second order in flc are integrable with the first power. Introduce the notation 

Assume that there exists a function M = Mij G L°° Qc), M,M G L°° Qc)y satisfying the equation (5.211) in the following sense. 

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