Existence and Uniqueness of an Rν-Generalized Solution of the Dirichlet Problem for the Lamé System with a Corner Singularity

Abstract

We consider the Dirichlet problem for the Lamé system in a two-dimensional domain whose boundary contains a reentrant corner. The notion of Rv-generalized solution is introduced for this problem. The existence and uniqueness of such a solution in the weighted set $${\mathop W\limits^\circ}_{2,v*}^1(\Omega,\delta)$$ is proved.