On some partial data Calderón type problems with mixed boundary conditions

In this article we consider the simultaneous recovery of bulk and boundary potentials in (degenerate) elliptic equations modelling conducting media with inaccessible boundaries. This connects local nonlocal Calderón type problems. We prove two main results on these problems: On one hand, derive Runge approximation results. Building these, deduce uniqueness for localized potentials. other construct a family CGO solutions associated corresponding equations. These allow us to arbitrary bounded, not necessarily The are constructed by duality new Carleman estimate.