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Volume 33, Issue 1
Explicit H1-Estimate for the Solution of the Lamé System with Mixed Boundary Conditions

Djamel Ait-Akli & Abdelkader Merakeb

DOI: 10.4208/jpde.v33.n1.5

J. Part. Diff. Eq., 33 (2020), pp. 64-92.

Published online: 2020-03

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  • 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.

  • Keywords

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

  • AMS Subject Headings

35J57, 74B05

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

djamel.aitakli@ummto.dz (Djamel Ait-Akli)

kader.merakeb@ummto.dz (Abdelkader Merakeb)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-33-64, author = {Ait-Akli , Djamel and Merakeb , Abdelkader}, title = {Explicit H1-Estimate for the Solution of the Lamé System with Mixed Boundary Conditions}, journal = {Journal of Partial Differential Equations}, year = {2020}, volume = {33}, number = {1}, pages = {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.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v33.n1.5}, url = {http://global-sci.org/intro/article_detail/jpde/15804.html} }
TY - JOUR T1 - Explicit H1-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 -

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.

Ait-Akli , Djamel and Merakeb , Abdelkader. (2020). Explicit H1-Estimate for the Solution of the Lamé System with Mixed Boundary Conditions. Journal of Partial Differential Equations. 33 (1). 64-92. doi:10.4208/jpde.v33.n1.5
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