On the asymptotic behavior of elliptic, anisotropic singularperturbations problems

Michel Chipot; Senoussi Guesmia

doi:10.3934/cpaa.2009.8.179

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2009, Volume 8, Issue 1: 179-193. Doi: 10.3934/cpaa.2009.8.179

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On the asymptotic behavior of elliptic, anisotropic singular perturbations problems

Michel Chipot^1, and
Senoussi Guesmia^2,

1.
University of Zürich, Institute of Mathematics, Winterthurerstrasse 190, CH-8057 Zürich
2.
University of Zürich, Institute of Mathematics, Winterthurerstrasse 190, CH-8057 Zurich

Received: June 2008

Revised: August 2008

Published: January 2009

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Abstract

In this paper, we consider anitropic singular perturbations of some elliptic boundary value problems. We study the asymptotic behavior as $\varepsilon \rightarrow 0$ for the solution. Strong convergence in some Sobolev spaces is proved and the rate of convergence in cylindrical domains is given.

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Mathematics Subject Classification: Primary: 35B25, 35B40; Secondary: 35J25.

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