RECENT UNIQUENESS RESULTS BY CAUCHY DATA ON ARBITRARY SUBBOUNDARY FOR 2-DIMENSIONAL ELLIPTIC EQUATIONS

I will present our recent results on the uniqueness in determining coefficients in 2-dimensional elliptic equations by all the set of
Cauchy data with Dirichlet data supported on arbitrary subboundary $\Gamma$ and Neumann data on $\Gamma$.
Classical Dirichlet-to-Neumann map corresponds to a special case where $\Gamma$ is the whole boundary, and our results are the best possible uniqueness results within some smoothness assumptions.