TY - JOUR
T1 - Explicit H<sup>1</sup>-Estimate for the Solution of the Lamé System with Mixed Boundary Conditions
AU - Ait-Akli , Djamel
AU - Merakeb , Abdelkader
JO - Journal of Partial Differential Equations
VL - 1
SP - 64
EP - 92
PY - 2020
DA - 2020/03
SN - 33
DO - http://doi.org/10.4208/jpde.v33.n1.5
UR - https://global-sci.org/intro/article_detail/jpde/15804.html
KW - Lamé system, Korn's inequality, Poincare's inequality, inequality of trace, explicit estimates.
AB - <p style="text-align: justify;">In this paper we consider the Lamé 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.</p>