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 ${\mathbb{R}}^n,n\ge 2$, 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.

20 pages

References in corpus (4)

• Reconstruction for the coefficients of a quasilinear elliptic partial differential equation
• Identification of a connection from Cauchy data on a Riemann surface with boundary
• Detection of Hermitian connections in wave equations with cubic non-linearity
• Uniqueness and stability of an inverse problem for a semi-linear wave equation

Cited by in corpus (3)

• Inverse problems for the fractional Laplace equation with lower order nonlinear perturbations
• An Inverse Problem for Non-linear Fractional Magnetic Schrodinger Equation
• A note on the partial data inverse problem for a nonlinear magnetic Schrödinger operator on Riemann surface