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ANALYTIC HYPOELLIPTICITY FOR SUMS OF SQUARES IN THE PRESENCE OF SYMPLECTIC NON TREVES STRATA

Part of: Partial differential equations Close-to-elliptic equations and systems

Published online by Cambridge University Press:  07 January 2019

Antonio Bove  and
Marco Mughetti
Antonio Bove
Affiliation:
Dipartimento di Matematica, Università di Bologna, Piazza di Porta San Donato 5, Bologna, Italy ([email protected]; [email protected])
Marco Mughetti
Affiliation:
Dipartimento di Matematica, Università di Bologna, Piazza di Porta San Donato 5, Bologna, Italy ([email protected]; [email protected])
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Abstract

In Albano, Bove and Mughetti [J. Funct. Anal. 274(10) (2018), 2725–2753]; Bove and Mughetti [Anal. PDE 10(7) (2017), 1613–1635] it was shown that Treves conjecture for the real analytic hypoellipticity of sums of squares operators does not hold. Models were proposed where the critical points causing a non-analytic regularity might be interpreted as strata. We stress that up to now there is no notion of stratum which could replace the original Treves stratum. In the proposed models such ‘strata’ were non-symplectic analytic submanifolds of the characteristic variety. In this note we modify one of those models in such a way that the critical points are a symplectic submanifold of the characteristic variety while still not being a Treves stratum. We show that the operator is analytic hypoelliptic.

Keywords

sums of squares of vector fieldsanalytic hypoellipticityTreves conjecture

MSC classification

Primary: 35H10: Hypoelliptic equations 35H20: Subelliptic equations
Secondary: 35B65: Smoothness and regularity of solutions 35A20: Analytic methods, singularities 35A27: Microlocal methods; methods of sheaf theory and homological algebra in PDE
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 19 , Issue 6 , November 2020 , pp. 1877 - 1888
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Copyright
© Cambridge University Press 2019

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