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Local solvability and hypoellipticity for semilinear anisotropic partial differential equations


Authors: Giuseppe de Donno and Alessandro Oliaro
Journal: Trans. Amer. Math. Soc. 355 (2003), 3405-3432
MSC (2000): Primary 35S05
DOI: https://doi.org/10.1090/S0002-9947-03-03275-6
Published electronically: April 11, 2003
MathSciNet review: 1974694
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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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Additional 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

DOI: https://doi.org/10.1090/S0002-9947-03-03275-6
Received by editor(s): February 7, 2001
Received by editor(s) in revised form: October 8, 2002
Published electronically: April 11, 2003
Article copyright: © Copyright 2003 American Mathematical Society

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