A note on the uniqueness from sets of positive measure for time dependent parabolic operators

TL;DR

This paper demonstrates how to achieve unique continuation from sets of positive measure for time-dependent parabolic equations with Lipschitz coefficients by combining existing results, extending known results from analytic coefficient cases.

Contribution

It extends the unique continuation property to parabolic equations with Lipschitz coefficients by synthesizing previous findings, broadening applicability beyond analytic cases.

Findings

Unique continuation from sets of positive measure established for Lipschitz parabolic operators.

Method combines existing results to generalize previous analytic coefficient results.

Applicable to equations with bounded lower order terms.

Abstract

The purpose of this short note is to show how it is possible to combine existing results in the literature to get the unique continuation from sets of positive measure for time dependent parabolic equations with Lipschitz principal part and bounded lower order terms, result which was known in the case of analytic coefficients in [3].