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

Abstract

SUMMARYBy 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 ÿrst and the second kind integral equations and the uniqueness and existence theorems are proved in various function spaces.

A boundary variational inequality approach to unilateral contact problems with friction for micropolar hemitropic solids

“…Thus from formula (19), the nonnegative function g T ∈ L ∞ (S C ). Consider the following unilateral mixed contact problem with friction.…”

“…The following assertion describes the null space of the energy density quadratic form E(U, U) (see [19]). 6 .…”

“…To reduce Problem (A) to a boundary variational inequality we need first to reduce the nonhomogeneous equation (20) and nonhomogeneous condition (21) to the homogeneous ones. To this purpose consider the following auxiliary linear mixed boundary value problem:…”

“…For real-valued vector functions U = (u, ) and U = (u , ) from the class [C 2 ( )] 6 the following Green formula holds [19] […”

“…where , , , , , , , , and are the material constants, see [7,19]. The equilibrium equations in the theory of hemitropic elasticity read as, see [7,19],…”