Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 10, pp. 1-14.

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

Authors: Aissa Aibeche   (Univ. de Setif, Algeria)
         Wided Chikouche (Univ. de Setif, Algeria)
	 Yasmina Daikh   (Universite de Jijel, Algeria)

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.