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GLOBAL HYPOELLIPTICITY OF SUMS OF SQUARES ON COMPACT MANIFOLDS

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

Published online by Cambridge University Press:  05 January 2024

Gabriel Araújo Open the ORCID record for Gabriel Araújo [Opens in a new window] ,
Igor A. Ferra Open the ORCID record for Igor A. Ferra [Opens in a new window]  and
Luis F. Ragognette Open the ORCID record for Luis F. Ragognette [Opens in a new window]
Gabriel Araújo*
Affiliation:
ICMC-USP, Universidade de São Paulo, São Carlos, SP, Brazil
Igor A. Ferra
Affiliation:
CMCC, Universidade Federal do ABC, São Bernardo do Campo, SP, Brazil ([email protected])
Luis F. Ragognette
Affiliation:
ICEx, Universidade Federal de Minas Gerais, Belo Horizonte, MG, Brazil ([email protected])
*
[email protected]
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Abstract

We present necessary and sufficient conditions for an operator of the type sum of squares to be globally hypoelliptic on $T \times G$, where T is a compact Riemannian manifold and G is a compact Lie group. These conditions involve the global hypoellipticity of a system of vector fields on G and are weaker than Hörmander’s condition, while generalizing the well known Diophantine conditions on the torus. Examples of operators satisfying these conditions in the general setting are provided.

Keywords

sums of squaresglobal hypoellipticityinvariant operators

MSC classification

Primary: 35H10: Hypoelliptic equations
Secondary: 35R01: Partial differential equations on manifolds 35R03: Partial differential equations on Heisenberg groups, Lie groups, Carnot groups, etc.
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 23 , Issue 5 , September 2024 , pp. 2405 - 2439
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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