Explicit H1-Estimate for the Solution of the Lamé System with Mixed Boundary Conditions (Journal of Partial Differential Equations, 2020)
"In this paper we consider the Lam\u00e9 system on a polygonal convex domain with mixed boundary conditions of Dirichlet-Neumann type. An explicit $L^2$ norm estimate for the gradient of the solution of this problem is established. This leads to an explicit bound of the $H^1$ norm of this solution. Note that the obtained upper-bound is not optimal."
Keywords: Lamé system; Korn's inequality; Poincare's inequality; inequality of trace; explicit estimates.