Hypoellipticity and local solvability of anisotropic PDEs with Gevrey nonlinearity

Giuseppe De Donno; Alessandro Oliaro

Bollettino dell'Unione Matematica Italiana (2006)

  • Volume: 9-B, Issue: 3, page 583-610
  • ISSN: 0392-4041

Abstract

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We propose a unified approach, based on methods from microlocal analysis, for characterizing the hypoellipticity and the local solvability in C ∞ and Gevrey G λ classes of semilinear anisotropic partial differential operators with Gevrey nonlinear perturbations, in dimension n ≥ 3 . The conditions for our results are imposed on the sign of the lower order terms of the linear part of the operator, see Theorem 1.1 and Theorem 1.3 below.

How to cite

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De Donno, Giuseppe, and Oliaro, Alessandro. "Hypoellipticity and local solvability of anisotropic PDEs with Gevrey nonlinearity." Bollettino dell'Unione Matematica Italiana 9-B.3 (2006): 583-610. <http://eudml.org/doc/289636>.

@article{DeDonno2006,
abstract = {We propose a unified approach, based on methods from microlocal analysis, for characterizing the hypoellipticity and the local solvability in $C^\infty$ and Gevrey $G^\lambda$ classes of semilinear anisotropic partial differential operators with Gevrey nonlinear perturbations, in dimension $n \geq 3$. The conditions for our results are imposed on the sign of the lower order terms of the linear part of the operator, see Theorem 1.1 and Theorem 1.3 below.},
author = {De Donno, Giuseppe, Oliaro, Alessandro},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {583-610},
publisher = {Unione Matematica Italiana},
title = {Hypoellipticity and local solvability of anisotropic PDEs with Gevrey nonlinearity},
url = {http://eudml.org/doc/289636},
volume = {9-B},
year = {2006},
}

TY - JOUR
AU - De Donno, Giuseppe
AU - Oliaro, Alessandro
TI - Hypoellipticity and local solvability of anisotropic PDEs with Gevrey nonlinearity
JO - Bollettino dell'Unione Matematica Italiana
DA - 2006/10//
PB - Unione Matematica Italiana
VL - 9-B
IS - 3
SP - 583
EP - 610
AB - We propose a unified approach, based on methods from microlocal analysis, for characterizing the hypoellipticity and the local solvability in $C^\infty$ and Gevrey $G^\lambda$ classes of semilinear anisotropic partial differential operators with Gevrey nonlinear perturbations, in dimension $n \geq 3$. The conditions for our results are imposed on the sign of the lower order terms of the linear part of the operator, see Theorem 1.1 and Theorem 1.3 below.
LA - eng
UR - http://eudml.org/doc/289636
ER -

References

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