Strong unique continuation for parabolic operators
Volume 154 / 2018
Colloquium Mathematicum 154 (2018), 1-14
MSC: Primary 35A02; Secondary 35K05.
DOI: 10.4064/cm7402-10-2017
Published online: 4 June 2018
Abstract
We prove a unique continuation theorem for functions $u$ vanishing to infinite order in the space-time variables at $(0,0)$ and satisfying the inequality $|\varDelta u+\partial _t u|\le V(x,t)|u|+W(x,t)|\nabla u|$ for some unbounded time-dependent $V$ and $W$ on ${\mathbb R}$, and in the radial case on $\mathbb R^n$.
