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Semiclassical analysis of a nonlinear eigenvalue problem and nonanalytic hypoellipticity


Authors: Bernard Helffer, Didier Robert and Xue Ping Wang
Translated by: the authors
Original publication: Algebra i Analiz, tom 16 (2004), nomer 1.
Journal: St. Petersburg Math. J. 16 (2005), 285-296
MSC (2000): Primary 35P30, 35P25
DOI: https://doi.org/10.1090/S1061-0022-04-00851-9
Published electronically: December 17, 2004
MathSciNet review: 2068356
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Abstract | References | Similar Articles | Additional Information

Abstract: A semiclassical analysis of a nonlinear eigenvalue problem arising from the study of the failure of analytic hypoellipticity is given. A general family of hypoelliptic, but not analytic hypoelliptic operators is obtained.


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Additional Information

Bernard Helffer
Affiliation: Département de Mathématiques, UMR CNRS 8628, Université Paris-Sud, Bat. 425, 91405 Orsay Cedex, France
Email: Bernard.Helffer@math.u-psud.fr

Didier Robert
Affiliation: Laboratoire de Mathématiques Jean Leray, Département de Mathématiques, UMR CNRS 6629, Université de Nantes, 44322 Nantes Cedex 3, France
Email: Didier.Robert@math.univ-nantes.fr

Xue Ping Wang
Affiliation: Laboratoire de Mathématiques Jean Leray, Département de Mathématiques, UMR CNRS 6629, Université de Nantes, 44322 Nantes Cedex 3, France
Email: Xue-Ping.Wang@math.univ-nantes.fr

DOI: https://doi.org/10.1090/S1061-0022-04-00851-9
Keywords: Semiclassical analysis, analytic hypoellipticity, nonlinear eigenvalue problem
Published electronically: December 17, 2004
Additional Notes: The first author was partially supported by the SPECT ESF European program. The third author was partially supported by the program “Outstanding Overseas Chinese Scholars” of the Chinese Academy of Sciences.
Dedicated: Dedicated to M. Sh. Birman on the occasion of his 75th birthday
Article copyright: © Copyright 2004 American Mathematical Society

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