A note of uniqueness on the Cauchy problem for Schrödinger or heat equations with degenerate elliptic principal parts
Hideki Takuwa (2004)
Bollettino dell'Unione Matematica Italiana
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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.