Backward Uniqueness of Kolmogorov Operators

Abstract

The backward uniqueness of the Kolmogorov operator $L={\sum }_{i,k=1}^n{\partial }_{x_i}(a_{i,k}(x,t){\partial }_{x_k})+{\sum }_{l=1}^m{x}_l{\partial }_{y_l}-{\partial }_t$, was proved in this paper. We obtained a weak Carleman inequality via Littlewood-Paley decomposition for the global backward uniqueness.

10 pages