Boundary value problems for the Lamé-Navier system in fractal domains

Abstract

The aim of this paper is to establish a representation formula for the solutions of the Lamé-Navier system in linear elasticity theory. We also study boundary value problems for such a system in a bounded domain $ \Omega\subset {\mathbb R}^3 $, allowing a very general geometric behavior of its boundary. Our method exploits the connections between this system and some classes of second order partial differential equations arising in Clifford analysis.

Keywords

• lamé-navier system
• linear elasticity
• fractal boundaries
• clifford analysis