Transmission problems in the theory of elastic hemitropic materials
David Natroshvili, Roland Gachechiladze, Avtandil Gachechiladze, Ioannis G. Stratis · Applicable Analysis · 2007
The purpose of this article is to investigate mixed transmission-boundary value problems for the differential equations of the theory of hemitropic (chiral) elastic materials. We consider the differential equations corresponding to the time harmonic dependent case, the so called pseudo-oscillation equations. Applying the potential method and the theory of pseudodifferential equations we prove uniqueness and existence theorems of solutions to the Dirichlet, Neumann and mixed transmission-boundary value problems for piecewise homogeneous hemitropic composite bodies and analyze their regularity properties. We investigate also interface crack problems and establish almost best regularity results.