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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

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Local solvability and hypoellipticity for semilinear anisotropic partial differential equations
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by Giuseppe de Donno and Alessandro Oliaro
Trans. Amer. Math. Soc. 355 (2003), 3405-3432
DOI: https://doi.org/10.1090/S0002-9947-03-03275-6
Published electronically: April 11, 2003

Abstract:

We propose a unified approach, based on methods from microlocal analysis, for characterizing the local solvability and hypoellipticity in $C^\infty$ and Gevrey $G^\sigma$ classes of $2$-variable semilinear anisotropic partial differential operators with multiple characteristics. The conditions imposed on the lower-order terms of the linear part of the operator are optimal.
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Bibliographic Information
  • Giuseppe de Donno
  • Affiliation: Dipartimento di Matematica, Università di Torino, Via Carlo Alberto 10, 10123 Torino, Italy
  • Email: dedonno@dm.unito.it
  • Alessandro Oliaro
  • Affiliation: Dipartimento di Matematica, Università di Torino, Via Carlo Alberto 10, 10123 Torino, Italy
  • Email: oliaro@dm.unito.it
  • Received by editor(s): February 7, 2001
  • Received by editor(s) in revised form: October 8, 2002
  • Published electronically: April 11, 2003
  • © Copyright 2003 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 355 (2003), 3405-3432
  • MSC (2000): Primary 35S05
  • DOI: https://doi.org/10.1090/S0002-9947-03-03275-6
  • MathSciNet review: 1974694