Quantitative strong unique continuation property for the Schr\"odinger operator with unbounded potential

TL;DR

This paper develops a quantitative strong unique continuation property for Schrödinger operators with unbounded potentials, extending previous results and combining local and global properties for broader applicability.

Contribution

It introduces a quantitative version of the strong unique continuation property for Schrödinger operators with unbounded potentials, building on and extending prior theoretical results.

Findings

Established a quantitative strong unique continuation property for unbounded potentials.

Combined local and global unique continuation results for broader implications.

Extended previous theoretical frameworks to unbounded potential cases.

Abstract

We revisit \cite[Theorem 6.3]{JK}. Following the main ideas used to prove this theorem, we establish a quantitative version of the strong unique continuation property for the Sch\"odinger operator with unbounded potential. We also show that a combination of this result with a global quantitative unique continuation property from an arbitrary interior data yields a global quantitative strong unique continuation.