Explicit H1-Estimate for the Solution of the Lamé System with Mixed Boundary Conditions

Abstract

"

In this paper we consider the Lam\u00e9 system on a polygonal convex domain \nwith mixed boundary conditions of Dirichlet-Neumann type. An explicit $L^2$ norm\nestimate for the gradient of the solution of this problem is established. This leads to an\nexplicit bound of the $H^1$ norm of this solution. Note that the obtained upper-bound is\nnot optimal.<\/p>"