On the Stability of the $C^\infty$-Hypoellipticity under Perturbations
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- by Cesare Parenti and Alberto Parmeggiani PDF
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Abstract:
We study the problem of perturbations of $C^\infty$-hypoelliptic operators by lower order terms. After giving several examples which show many different possibilities, we then prove a stability result which shows that a hypoelliptic linear partial differential operator $P$ which loses finitely many derivatives and whose formal adjoint $P^*$ is still hypoelliptic (but with no assumption on the loss of derivatives) remains hypoelliptic with the same loss of derivatives after perturbation by a lower order linear partial differential operator (whose order depends on the loss of derivatives).References
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Additional Information
- Cesare Parenti
- Affiliation: Department of Computer Science, University of Bologna, Via Mura Anteo Zamboni 7, 40126 Bologna, Italy
- MR Author ID: 136150
- Alberto Parmeggiani
- Affiliation: Department of Mathematics, University of Bologna, Piazza di Porta S. Donato 5, 40126 Bologna, Italy
- MR Author ID: 267489
- Email: alberto.parmeggiani@unibo.it
- Received by editor(s): April 12, 2017
- Published electronically: September 13, 2017
- Communicated by: Michael Hitrik
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 1097-1104
- MSC (2010): Primary 35H10; Secondary 35A08, 35B35
- DOI: https://doi.org/10.1090/proc/13800
- MathSciNet review: 3750221