Abstract

Let t T be a bounded 3D domain with Lipschitz boundary (Gamma) , (sigma) equals (pi) R 2 is a prescribed displacement on (Gamma) (volume forces are absent). We denote by A(u,v) equals integral (Omega ) L(epsilon) (u) (DOT) (epsilon) (v) dx bilinear form corresponding to the first elasticity problem where L is a tensor of Hooke's law written in the tensor form (sigma) equals L(epsilon) (isotropic case will be the subject of consideration) and by V a subspace of Sobolev space W 2 1 ((Omega) ,R 3 ) that is V equals {v equalsV W 2 1 ((Omega) ,R 3 ) v equals 0 on (Gamma) }. We assume that g i equalsV W 2 1/2 ((Gamma) ) and A(u,v) is V-elliptic bilinear form. A weak solution of the first elasticity problem is a vector- valued function.

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