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On the Stability of the $ C^\infty$-Hypoellipticity under Perturbations

Authors: Cesare Parenti and Alberto Parmeggiani
Journal: Proc. Amer. Math. Soc. 146 (2018), 1097-1104
MSC (2010): Primary 35H10; Secondary 35A08, 35B35
Published electronically: September 13, 2017
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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).

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Additional Information

Cesare Parenti
Affiliation: Department of Computer Science, University of Bologna, Via Mura Anteo Zamboni 7, 40126 Bologna, Italy

Alberto Parmeggiani
Affiliation: Department of Mathematics, University of Bologna, Piazza di Porta S. Donato 5, 40126 Bologna, Italy

Keywords: $C^\infty$-hypoellipticity, hypoellipticity with loss of derivatives, fundamental solution
Received by editor(s): April 12, 2017
Published electronically: September 13, 2017
Communicated by: Michael Hitrik
Article copyright: © Copyright 2017 American Mathematical Society

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