Real interpolation spaces between the domain of the Laplace operator with transmission conditions and L^p on a polygonal domain
Aissa Aibèche, Wided Chikouche, Yasmina Daikh · DOAJ (DOAJ: Directory of Open Access Journals) · 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.