Quantitative unique continuation for the heat equation with Coulomb potentials

TL;DR

This paper develops a quantitative unique continuation estimate for heat equations with Coulomb potentials, using frequency function methods and Hardy inequalities, applicable in smooth or convex domains.

Contribution

It introduces a new quantitative estimate for the heat equation with Coulomb potentials, extending unique continuation results with explicit bounds.

Findings

Established a Hölder-type estimate for solutions.

Applied frequency function and Hardy inequalities in the analysis.

Results are valid in smooth or convex domains.

Abstract

In this paper, we establish a H\"older-type quantitative estimate of unique continuation for solutions to the heat equation with Coulomb potentials in either a bounded convex domain or a $C^2$-smooth bounded domain. The approach is based on the frequency function method, as well as some parabolic-type Hardy inequalities.