AN INVERSE PROBLEM WITH PARTIAL NEUMANN DATA AND Ln/2 POTENTIALS

We consider a partial data Calderon 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 triangle + q can uniquely determine q is an element of L-n/2(ohm). 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.