Rohit Khandelwal

On the $W^{2,p}$ solvability for mixed boundary value problems

We establish global $W^{2,p}$ solvability for the Poisson equation with mixed Dirichlet--Neumann boundary conditions in two classes of domains in all dimensions $n\geq 2$. For $C^{1,\alpha}$ domains with a Reifenbeg flat interface, we obtain the optimal range $11-1/p$. For Lipschitz polyhedra with facewise boundary dec...