Electron. J. Diff. Equ., Vol. 2012 (2012), No. 10, pp. 1-14.

Real interpolation spaces between the domain of the Laplace operator with transmission conditions and L^p on a polygonal domain

Aissa Aibeche, Wided Chikouche, Yasmina Daikh

Abstract:
We provide a description of the real interpolation spaces between the domain of the Laplace operator (with transmission conditions in a polygonal domain $\Omega$) and $L^p(\Omega)$ as interpolation spaces between $\mathcal{W}^{2,p}(\Omega)$ (possibly augmented with singular solutions) and $L^p(\Omega)$. This result relies essentially on estimates on the resolvent and the reiteration theorem.

Submitted April 10, 2011. Published January 13, 2012.
Math Subject Classifications: 35R05, 35A20, 46B70.
Key Words: Transmission problem; non-smooth domains; interpolation.

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Aissa Aibeche
Université de Setif
Département de Mathéematiques
Faculté des Sciences
Setif 19000, Algeria
email: aibeche@univ-setif.dz
Wided Chikouche
Université de Jijel
Laboratoire de Mathématiques Pures et Appliquées
B.P. 98, Ouled Aissa, 18000 Jijel, Algeria
email: w_chikouche@yahoo.com
Yasmina Daikh
Université de Jijel
Laboratoire de Mathématiques Pures et Appliquées
B.P. 98, Ouled Aissa, 18000 Jijel, Algeria
email: yasmina_daikh@yahoo.fr

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