Transmission problems in the theory of elastic hemitropic materials

Abstract

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.

Keywords:

• Elasticity theory
• Elastic hemitropic materials
• Transmission-boundary value problems
• Potential theory

Keywords:

• 2000 Mathematics Subject Classifications
• 74H20
• 35J55

Acknowledgements

This research was supported by the Georgian National Science Foundation (GNSF) grant No. GNSF/ST06/3-001.