Unique continuation for second-order parabolic operators at the initial time
Paolo G. Albano, Daniel Tataru · Proceedings of the American Mathematical Society · 2003
We consider second-order parabolic equations with time independent coefficients. Under reasonable assumptions, it is known that the fundamental solution satisfies certain Gaussian bounds related to the associated geodesic distance. In this article we prove a sharp unique continuation property at the initial time which matches exactly the above-mentioned kernel bounds.