Geodesic
Real interpolation spaces between the domain of the Laplace operator with transmission conditions and $L^p$ on a polygonal domain
Electronic Journal of Differential Equations, Tome 2012 (2012).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 35R05, 35A20, 46B70
Keywords: transmission problem, non-smooth domains, interpolation 
@article{EJDE_2012__2012__a27,
     author = {Aibeche, Aissa and Chikouche, Wided and Daikh, Yasmina},
     title = {Real interpolation spaces between the domain of the {Laplace} operator with transmission conditions and $L^p$ on a polygonal domain},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2012},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a27/}
}
TY  - JOUR
AU  - Aibeche, Aissa
AU  - Chikouche, Wided
AU  - Daikh, Yasmina
TI  - Real interpolation spaces between the domain of the Laplace operator with transmission conditions and $L^p$ on a polygonal domain
JO  - Electronic Journal of Differential Equations
PY  - 2012
VL  - 2012
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a27/
LA  - en
ID  - EJDE_2012__2012__a27
ER  - 
%0 Journal Article
%A Aibeche, Aissa
%A Chikouche, Wided
%A Daikh, Yasmina
%T Real interpolation spaces between the domain of the Laplace operator with transmission conditions and $L^p$ on a polygonal domain
%J Electronic Journal of Differential Equations
%D 2012
%V 2012
%I mathdoc
%U http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a27/
%G en
%F EJDE_2012__2012__a27
Aibeche, Aissa; Chikouche, Wided; Daikh, Yasmina. Real interpolation spaces between the domain of the Laplace operator with transmission conditions and $L^p$ on a polygonal domain. Electronic Journal of Differential Equations, Tome 2012 (2012). http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a27/