Corner Singularities and Regularity of Weak Solutions for the Two-Dimensional Lamé Equations on Domains with Angular Corners

This paper is concerned with corner singularities of weak solutions of boundary value problems in the theory of plane linearized elasticity. The presence of angular corner points or points at which the type of boundary conditions changes yields generally local singularities in the solution. This singular behavior in the vicinity of such points can be described with the help of asymptotic singular representations for the solution, which essentially depend on the zeros of certain transcendental functions. These transcendental functions will be derived and analyzed for all ten possible combinations of boundary conditions, generated by the four basic ones, prescribing in the tangential and normal direction of the boundary, respectively, either the displacement or the tractions. The regularity of the corresponding weak solutions will be investigated. This revised version was published online in July 2006 with corrections to the Cover Date.