Basic boundary value problems of thermoelasticity for anisotropic bodies with cuts. II
Roland Duduchava, David Natroshvili, Eugene Shargorodsky · Georgian Mathematical Journal · 1995
In the first part [1] of the paper the basic boundary value problems of the mathematical theory of elasticity for three-dimensional anisotropic bodies with cuts were formulated. It is assumed that the two-dimensional surface of a cut is a smooth manifold of an arbitrary configuration with a smooth boundary. The existence and uniqueness theorems for boundary value problems were formulated in the Besov $$(\mathbb{B}_{p, q}^s )$$ and Bessel-potential (ℍ ) spaces. In the present part we give the proofs of the main results (Theorems 7 and 8) using the classical potential theory and the nonclassical theory of pseudodifferential equations on manifolds with a boundary.