Quantitative uniqueness for parabolic equations with H\"older potentials

TL;DR

This paper establishes a quantitative uniqueness result for parabolic equations with H"older potentials, bridging previous estimates and extending recent results to time-dependent operators.

Contribution

It generalizes existing uniqueness estimates to parabolic operators with H"older potentials, interpolating between known bounds and extending prior work.

Findings

Derives a space-like quantitative uniqueness estimate for parabolic operators.

Interpolates between Donnelly-Fefferman and Bourgain-Kenig estimates.

Extends recent results from time-independent Schr"odinger operators to parabolic equations.

Abstract

In this note we derive a space-like quantitative uniqueness result for parabolic operators with H\"older zero-order term that interpolates between the Donnelly-Fefferman and the Bourgain-Kenig estimate. This generalizes a recent result of Teng, Wang and Zhu for the time-independent Schr\"odinger operator with a H\"older potential.