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

Authors

  • Djamel Ait-Akli L2CSP, Mouloud Mammeri University Tizi-Ouzou, 15000, Algeria.
  • Abdelkader Merakeb L2CSP, Mouloud Mammeri University Tizi-Ouzou, 15000, Algeria.

DOI:

https://doi.org/10.4208/jpde.v33.n1.5

Keywords:

Lamé system, Korn's inequality, Poincare's inequality, inequality of trace, explicit estimates.

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>"

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Published

2020-05-12

Issue

Vol. 33 No. 1 (2020)

Section

Articles