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2017 Analytic hypoellipticity for sums of squares and the Treves conjecture, II
Antonio Bove, Marco Mughetti
Anal. PDE 10(7): 1613-1635 (2017). DOI: 10.2140/apde.2017.10.1613


We are concerned with the problem of real analytic regularity of the solutions of sums of squares with real analytic coefficients. The Treves conjecture defines a stratification and states that an operator of this type is analytic hypoelliptic if and only if all the strata in the stratification are symplectic manifolds.

Albano, Bove, and Mughetti (2016) produced an example where the operator has a single symplectic stratum, according to the conjecture, but is not analytic hypoelliptic.

If the characteristic manifold has codimension 2 and if it consists of a single symplectic stratum, defined again according to the conjecture, it has been shown that the operator is analytic hypoelliptic.

We show here that the above assertion is true only if the stratum is single, by producing an example with two symplectic strata which is not analytic hypoelliptic.


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Antonio Bove. Marco Mughetti. "Analytic hypoellipticity for sums of squares and the Treves conjecture, II." Anal. PDE 10 (7) 1613 - 1635, 2017.


Received: 1 June 2016; Revised: 24 February 2017; Accepted: 17 June 2017; Published: 2017
First available in Project Euclid: 16 November 2017

zbMATH: 1375.35094
MathSciNet: MR3683923
Digital Object Identifier: 10.2140/apde.2017.10.1613

Primary: 35H10 , 35H20
Secondary: 35A20 , 35A27 , 35B65

Keywords: analytic hypoellipticity , sums of squares of vector fields , Treves conjecture

Rights: Copyright © 2017 Mathematical Sciences Publishers


Vol.10 • No. 7 • 2017
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