Local compactness for linear elasticity in irregular domains

For the theory of boundary value problems in linear elasticity, it is of crucial importance that the space of vector-valued L²-functions whose symmetrized Jacobians are square-integrable should be compactly embedded in L². For regions with the cone property this is usually achieved by combining Korn's inequalities and Rellich's selection theorem. We shall show that in a class of less regular regions Korn's second inequality fails whereas the desired compact embedding still holds true.