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
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},
year = {2004},
volume = {Ser. 8, 7B},
number = {3},
zbl = {1178.35187},
mrnumber = {MR2101662},
language = {en},
url = {http://geodesic.mathdoc.fr/item/BUMI_2004_8_7B_3_a12/}
}
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 della Unione matematica italiana PY - 2004 SP - 731 EP - 744 VL - 7B IS - 3 UR - http://geodesic.mathdoc.fr/item/BUMI_2004_8_7B_3_a12/ LA - en ID - BUMI_2004_8_7B_3_a12 ER -
%0 Journal Article %A Takuwa, Hideki %T A note of uniqueness on the Cauchy problem for Schrödinger or heat equations with degenerate elliptic principal parts %J Bollettino della Unione matematica italiana %D 2004 %P 731-744 %V 7B %N 3 %U http://geodesic.mathdoc.fr/item/BUMI_2004_8_7B_3_a12/ %G en %F BUMI_2004_8_7B_3_a12
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/