Geodesic
Three cylinder inequalities and unique continuation properties for parabolic equations
Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 13 (2002) no. 2, pp. 107-120.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

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 $S$.
Dimostriamo la seguente propriet`a di continuazione unica. Sia $u$ una soluzione di un’equazione parabolica lineare del secondo ordine e $S$ un segmento parallelo all’asse $t$. Se $u$ ha uno zero di ordine maggiore di qualsiasi polinomio non costante e indipendente dal tempo allora $u$ si annulla in ogni punto, $(x,t^{\prime})$, tale che il piano $t = t^{\prime}$ intersechi $S$. 
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Vessella, Sergio. Three cylinder inequalities and unique continuation properties for parabolic equations. Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 13 (2002) no. 2, pp. 107-120. http://geodesic.mathdoc.fr/item/RLIN_2002_9_13_2_a5/

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