Backward uniqueness for general parabolic operators in the whole space

TL;DR

This paper establishes backward uniqueness for a broad class of second-order parabolic operators in the entire space, under specific regularity and decay conditions on the coefficients, extending classical and recent results.

Contribution

It generalizes backward uniqueness results for parabolic operators with less restrictive coefficient regularity and decay assumptions.

Findings

Backward uniqueness holds under Lipschitz continuity of coefficients.

Results extend classical theorems by Lions and Malgrange.

The paper covers operators with coefficients satisfying decay conditions.

Abstract

We prove the backward uniqueness for general parabolic operators of second order in the whole space under assumptions that the leading coefficients of the operator are Lipschitz and their gradients satisfy certain decay conditions. This result extends in some ways a classical result of Lions and Malgrange [12] and a recent result of the authors [10].