Square roots of divergence operators]{The square root problem for second order, divergence form operators with mixed boundary conditions on $L^p$
Résumé
We show that, under very general conditions on the domain $\Omega$ and the Dirichlet part $D$ of the boundary, the operator $\bigl (-\nabla \cdot \mu \nabla +1\bigr )^{1/2}$ with mixed boundary conditions provides a topological isomorphism between $W^{1,p}_D(\Omega)$ and $L^p(\Omega)$, if $p \in {]1,2]}$.
Origine : Fichiers produits par l'(les) auteur(s)