The square root problem for second order, divergence form operators with mixed boundary conditions on $L^p$
The square root problem for second order, divergence form operators with mixed boundary conditions on $L^p$
We show that, under general conditions, 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 $L^p(\Omega)$, for $p \in {]1,2[}$ if one presupposes that this isomorphism holds true for $p=2$. The domain $\Omega$ is assumed to be bounded, the Dirichlet …