A remark on the local uniqueness by the monotonicity based method for the magnetic Schrödinger equation

Ryusei Yamashita

doi:10.3934/cpaa.2023077

Article Contents

2023, Volume 22, Issue 8: 2547-2558. Doi: 10.3934/cpaa.2023077

This issue Previous Article On a class of nonlinear evolution inequalities of convolution type on Riemannian manifolds Next Article The Wellposedness and controllability of the generalized symmetric regularized long wave system

A remark on the local uniqueness by the monotonicity based method for the magnetic Schrödinger equation

Ryusei Yamashita

Department of Mathematical Sciences, Tokyo Metropolitan University, Minami-Ohsawa 1-1, Hachioji, Tokyo, 192-0397 Japan

Received: December 2022

Revised: February 2023

Early access: May 2023

Published: August 2023

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Abstract

In this paper, we prove a local uniqueness by the monotonicity based method for a potential $ q $ of the magnetic Schrödinger operator $ -D^2_A u +q u = 0 $ in a bounded domain $ \Omega $ from partial boundary data. Moreover, we give monotonicity tests to detect an unknown obstacle for the magnetic Schrödinger equation.

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Mathematics Subject Classification: Primary: 35Q40, 35R30.

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