Mathematical problems of the theory of elasticity of chiral materials for Lipschitz domains

By the potential method, we investigate the Dirichlet and Neumann boundary value problems of the elasticity theory of hemitropic (chiral) materials in the case of Lipschitz domains. We study properties of the single- and double-layer potentials and of certain, generated by them, boundary integral operators. These results are applied to reduce the boundary value problems to the equivalent first and the second kind integral equations and the uniqueness and existence theorems are proved in various function spaces.