On the linearized system of elasticity in the half-space

Abstract

The purpose of this paper is twofold. The first goal is to provide a simple and constructive proof of Korn inequalities in half-space with weighted norms. The proof leads to explicit values of the constants. The second objective is to use these inequalities to show that the linear elasticity system in half-space admits a coercive variational formulation. This formulation corresponds to the physical case in which the solution is evanescent at infinity.

Keywords

• linear elasticity
• unbounded domains
• korn's inequality
• half-space
• weighted spaces