Geodesic
A note of uniqueness on the Cauchy problem for Schrödinger or heat equations with degenerate elliptic principal parts
Bollettino della Unione matematica italiana, Série 8, 7B (2004) no. 3, pp. 731-744

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

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. 
@article{BUMI_2004_8_7B_3_a12,
     author = {Takuwa, Hideki},
     title = {A note of uniqueness on the {Cauchy} problem for {Schr\"odinger} or heat equations with degenerate elliptic principal parts},
     journal = {Bollettino della Unione matematica italiana},
     pages = {731--744},
     publisher = {mathdoc},
     volume = {Ser. 8, 7B},
     number = {3},
     year = {2004},
     zbl = {1178.35187},
     mrnumber = {MR2101662},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2004_8_7B_3_a12/}
}
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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 della Unione matematica italiana, Série 8, 7B (2004) no. 3, pp. 731-744. http://geodesic.mathdoc.fr/item/BUMI_2004_8_7B_3_a12/