Abstract

In this talk, we will discuss sharp estimate of the order of vanishing of solutions to parabolic equations with variable coefficients. For real-analytic leading coefficients, we will present localised estimate of the nodal set, at a given time-level, that generalises the celebrated one of Donnelly and Fefferman. We will also discuss Landis type results for global solutions. This is based on joint work with Agnid Banerjee and Nicola Garofalo.