On homogenization of solutions of the poisson equation in a perforated domain with different types of boundary conditions on different cavities

In this paper we consider boundary value problems in perforated domains with periodic structures and cavities of different scales, with the Neumann condition on some of them and mixed boundary conditions on others. We take a case when cavities with mixed boundary conditions have so called critical s...

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Hauptverfasser: Jäger, Willi (VerfasserIn) , Olejnik, Olʹga A. (VerfasserIn) , Shaposhnikova, Tat'yana Ardolionovna (VerfasserIn)
Dokumenttyp: Article (Journal)
Sprache:Englisch
Veröffentlicht: 1997
In: Applicable analysis
Year: 1997, Jahrgang: 65, Heft: 3/4, Pages: 205-223
ISSN:1563-504X
DOI:10.1080/00036819708840559
Online-Zugang:Resolving-System, Volltext: http://dx.doi.org/10.1080/00036819708840559
Verlag, Volltext: https://www.tandfonline.com/doi/abs/10.1080/00036819708840559
Volltext
Verfasserangaben:W. Jäger, O.A. Oleinik, T.A. Shaposhnikova

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520 |a In this paper we consider boundary value problems in perforated domains with periodic structures and cavities of different scales, with the Neumann condition on some of them and mixed boundary conditions on others. We take a case when cavities with mixed boundary conditions have so called critical size (see [1]) and cavities with the Neumann conditions have the scale of the cell. In the same way other cases can be studied, when we have the Neumann and the Dirichlet boundary conditions or the Dirichlet condition and the mixed boundary condition on the boundary of cavities.There is a large literature where homogenization problems in perforated domains were studied [2];-[7]; 
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