An inverse problem with partial Neumann data and L^n/2 potentials

We consider a partial data Calderón problem for elliptic boundary value problems with unbounded coefficients. In particular, we will show that partial measurement of the Neumann-Dirichlet data for the operator Δ + q can uniquely determine q ε L n/2 (Ω) . This requires that we construct an explicit Green's function for the conjugated Laplacian with specified Neumann boundary conditions. The explicit construction of the Green's function allows us to deduce L^p type estimates which would otherwise be out of reach using the previous methods for constructing such Green's functions for bounded potentials.