Explicit H<sup>1</sup>-Estimate for the Solution of the Lamé System with Mixed Boundary Conditions

Explicit H<sup>1</sup>-Estimate for the Solution of the Lamé System with Mixed Boundary Conditions

Year:    2020

Author:    Djamel Ait-Akli, Abdelkader Merakeb

Journal of Partial Differential Equations, Vol. 33 (2020), Iss. 1 : pp. 64–92

Abstract

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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

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

Journal of Partial Differential Equations, Vol. 33 (2020), Iss. 1 : pp. 64–92

Published online:    2020-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    29

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

Author Details

Djamel Ait-Akli

Abdelkader Merakeb