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)
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},
     year = {2012},
     volume = {2012},
     zbl = {1251.46007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a27/}
}
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%A Daikh,  Yasmina
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%J Electronic journal of differential equations
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%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/