Hardy's uncertainty principle and unique continuation property for stochastic heat equations

TL;DR

This paper establishes a uniqueness result for stochastic heat equations with random potentials, extending Hardy's uncertainty principle to stochastic heat evolutions, highlighting the conditions under which solutions are uniquely determined.

Contribution

It introduces a novel stochastic version of Hardy's uncertainty principle, providing a new uniqueness criterion for stochastic heat equations with random potentials.

Findings

Proves a stochastic Hardy's uncertainty principle.

Establishes unique continuation properties for stochastic heat equations.

Provides conditions ensuring solution uniqueness.

Abstract

The goal of this paper is to prove a uniqueness result for a stochastic heat equation with a randomly perturbed potential, which can be considered as a variant of Hardy's uncertainty principle for stochastic heat evolutions.