A note of uniqueness on the Cauchy problem for Schrödinger or heat equations with degenerate elliptic principal parts
Takuwa, Hideki
Bollettino dell'Unione Matematica Italiana, Tome 7-A (2004), p. 731-744 / Harvested from Biblioteca Digitale Italiana di Matematica
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We study the local uniqueness in the Cauchy problem for Schrödinger or heat equations whose principal parts are nonnegative. We show the compact uniqueness under a weak form of pseudo convexity. This makes up for the known results under the conormal pseudo convexity given by Tataru, Hörmander, Robbiano- Zuily and L. T'Joen. Our method is based on a kind of integral transform and a weak form of Carleman estimate for degenerate elliptic operators.

In questo articolo studiamo la locale unicità nel problema di Cauchy per equazioni di Schrödinger o del calore con parte principale non negativa. Otteniamo l'unicità compatta sotto la condizione di una forma debole di pseudo convessità. Questo si collega ai risultati noti in ipotesi di pseudo convessità conormale ottenuti da Tataru, Hörmander, Robbiano-Zuily e L. T'Joen. Il nostro metodo si basa su di un tipo di trasformazione integrale ed una forma debole di stime di Carleman per operatori ellittici degeneri.

Publié le : 2004-10-01
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     author = {Hideki Takuwa},
     title = {A note of uniqueness on the Cauchy problem for Schr\"odinger or heat equations with degenerate elliptic principal parts},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {7-A},
     year = {2004},
     pages = {731-744},
     zbl = {1178.35187},
     mrnumber = {2101662},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2004_8_7B_3_731_0}
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Takuwa, Hideki. A note of uniqueness on the Cauchy problem for Schrödinger or heat equations with degenerate elliptic principal parts. Bollettino dell'Unione Matematica Italiana, Tome 7-A (2004) pp. 731-744. http://gdmltest.u-ga.fr/item/BUMI_2004_8_7B_3_731_0/

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