Three cylinder inequalities and unique continuation properties for parabolic equations

Vessella, Sergio

Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 13 (2002) no. 2, pp. 107-120

Résumé

We prove the following unique continuation property. Let $u$ be a solution of a second order linear parabolic equation and $S$ a segment parallel to the $t$-axis. If $u$ has a zero of order faster than any non constant and time independent polynomial at each point of $S$ then $u$ vanishes in each point, $(x,t^{\prime})$, such that the plane $t = t^{\prime}$ has a non empty intersection with $S$.