A new approach for the strong unique continuation of electromagnetic Schroedinger operator with complex-valued coefficient

TL;DR

This paper establishes a strong unique continuation property for electromagnetic Schrödinger operators with complex coefficients, using multipliers and a priori estimates, and demonstrates its application in boundary control problems.

Contribution

It introduces a novel method employing multipliers to prove unique continuation for complex-valued electromagnetic Schrödinger operators, linking it to controllability.

Findings

Proved strong unique continuation property for complex electromagnetic Schrödinger operators.

Developed a priori estimates using physical multipliers.

Applied results to boundary controllability, showing boundary data determines interior values.

Abstract

This paper mainly addresses the strong unique continuation property for the electromagnetic Schr\"{o}dinger operator with complex-valued coefficients. Appropriate multipliers with physical backgrounds have been introduced to prove a priori estimates. Moreover, its application in an exact controllability problem has been shown, in which case, the boundary value determines the interior value completely.