# A note of uniqueness on the Cauchy problem for Schrödinger or heat equations with degenerate elliptic principal parts

Bollettino dell'Unione Matematica Italiana (2004)

- Volume: 7-B, Issue: 3, page 731-744
- ISSN: 0392-4041

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topTakuwa, Hideki. "A note of uniqueness on the Cauchy problem for Schrödinger or heat equations with degenerate elliptic principal parts." Bollettino dell'Unione Matematica Italiana 7-B.3 (2004): 731-744. <http://eudml.org/doc/195272>.

@article{Takuwa2004,

abstract = {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.},

author = {Takuwa, Hideki},

journal = {Bollettino dell'Unione Matematica Italiana},

language = {eng},

month = {10},

number = {3},

pages = {731-744},

publisher = {Unione Matematica Italiana},

title = {A note of uniqueness on the Cauchy problem for Schrödinger or heat equations with degenerate elliptic principal parts},

url = {http://eudml.org/doc/195272},

volume = {7-B},

year = {2004},

}

TY - JOUR

AU - Takuwa, Hideki

TI - A note of uniqueness on the Cauchy problem for Schrödinger or heat equations with degenerate elliptic principal parts

JO - Bollettino dell'Unione Matematica Italiana

DA - 2004/10//

PB - Unione Matematica Italiana

VL - 7-B

IS - 3

SP - 731

EP - 744

AB - 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.

LA - eng

UR - http://eudml.org/doc/195272

ER -

## References

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- DEL SANTO, D., A Carleman estimate for degenerate elliptic operators with an application to an illposed problem, Boll. U. M. I., 11-B (1997), 327-339. Zbl0877.35051MR1459281
- TARAMA, S., On the estimate of some conjugation, preprint.
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- ZUILY, C., Uniqueness and Non-uniqueness in the Cauchy Problem, Progress in Math.33, Birkhäuser, 1983. Zbl0521.35003

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