Partial data inverse problems for nonlinear magnetic Schrödinger equations

Abstract

We prove that the knowledge of the Dirichlet-to-Neumann map, measured on a part of the boundary of a bounded domain in $\mathbb{R}^n , n \geq 2$, can uniquely determine, in a nonlinear magnetic Schrödinger equation, the vector-valued magnetic potential and the scalar electric potential, both being nonlinear in the solution.