Mathematical Research Letters

Volume 30 (2023)

Number 5

Partial data inverse problems for nonlinear magnetic Schrödinger equations

Pages: 1535 – 1563

DOI: https://dx.doi.org/10.4310/MRL.2023.v30.n5.a10

Authors

Ru-Yu Lai (School of Mathematics, University of Minnesota, Minneapolis, Minn., U.S.A.)

Ting Zhou (Department of Mathematics, Northeastern University, Boston, Massachusetts, U.S.A.)

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.

Full Text (PDF format)

R.-Y. Lai is partially supported by the NSF grant DMS-1714490 and DMS-2006731.

Received 6 June 2021

Received revised 10 October 2021

Accepted 26 October 2021

Published 14 May 2024