Determining an unbounded potential for an elliptic equation with a power type nonlinearity

Abstract

In this article we focus on inverse problems for a semilinear elliptic equation. We show that a potential q in Ln/2+ε, ε>0, can be determined from the full and partial Dirichlet-to-Neumann map. This extends the results from [20] where this is shown for Hölder continuous potentials. Also we show that when the Dirichlet-to-Neumann map is restricted to one point on the boundary, it is possible to determine a potential q in Ln+ε. The authors of [25] proved this to be true for Hölder continuous potentials.