Three cylinder inequalities and unique continuation properties for parabolic equations

Vessella, Sergio

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 13 (2002), p. 107-120 / Harvested from Biblioteca Digitale Italiana di Matematica

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Abstract
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, $(x, t^{'})$ , such that the plane $t = t^{'}$ 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, $(x, t^{'})$ , tale che il piano $t = t^{'}$ intersechi $S$ .

Publié le : 2002-06-01

MR 1949484 | Zbl 1221.35181

@article{RLIN_2002_9_13_2_107_0,
     author = {Sergio Vessella},
     title = {Three cylinder inequalities and unique continuation properties for parabolic equations},
     journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
     volume = {13},
     year = {2002},
     pages = {107-120},
     zbl = {1221.35181},
     mrnumber = {1949484},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RLIN_2002_9_13_2_107_0}
}

Vessella, Sergio. Three cylinder inequalities and unique continuation properties for parabolic equations. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 13 (2002) pp. 107-120. http://gdmltest.u-ga.fr/item/RLIN_2002_9_13_2_107_0/

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