Über ebene Bimetallprobleme mit verschiedenen Kontaktbedingungen und Dirichletschen Randbedingungen

Abstract

Existence and uniqueness theorems for boundary contact problems of plane elastostatics are proved. The special quality is that the line between two elastical homogeneous parts reaches to the external boundary $S$ of the whole domain. Three different contact conditions and Dirichlet boundary conditions (displacement vector on $S$ given) are considered. The problem is reduced with the aid of potentials, which have Green’s contact tensors in the kernel, to systems of singular integral equations about $S$ containing Cauchy-type integrals and integrals with fixed singularities. From the theory of Duduchava it follows that the occuring integral operators are Fredholm operators in the space $L_2(S)$ and have index zero. The null spaces of these operators contain only the zero.