Global solvability and global hypoellipticity for a class of complex vector fields on the 3-torus

DOI10.1007/s11868-015-0121-0zbMath1336.35124OpenAlexW652810822MaRDI QIDQ496827

Paulo L. Dattori da Silva, Alexandre Kirilov, Adalberto Panobianco Bergamasco, Rafael Borro Gonzalez

Publication date: 22 September 2015

Published in: Journal of Pseudo-Differential Operators and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11868-015-0121-0

zbMATH Keywords

Diophantine condition

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Periodic solutions to PDEs (35B10) Linear first-order PDEs (35F05) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Hypoelliptic equations (35H10)

Related Items (12)

Global hypoellipticity for first-order operators on closed smooth manifolds ⋮ Partial Fourier series on compact Lie groups ⋮ Global solvability and global hypoellipticity in Gevrey classes for vector fields on the torus ⋮ On certain non-hypoelliptic vector fields with finite-codimensional range on the three-torus ⋮ Existence and regularity of periodic solutions to certain first-order partial differential equations ⋮ Global hypoellipticity for a class of pseudo-differential operators on the torus ⋮ Existence of global solutions for a class of vector fields on the three-dimensional torus ⋮ Existence and regularity of periodic solutions for a class of partial differential operators ⋮ Solvability of a class of first order differential operators on the torus ⋮ Global hypoellipticity for strongly invariant operators ⋮ Global properties of vector fields on compact Lie groups in Komatsu classes ⋮ Perturbations of globally hypoelliptic operators on closed manifolds

Cites Work

• Study of a model in the theory of complexes of pseudodifferential operators
• Perturbations of globally hypoelliptic operators
• Global Solvability for a Class of Complex Vector Fields on the Two-Torus
• Globally Hypoelliptic Vector Fields on Compact Surfaces
• Globally Hypoelliptic and Globally Solvable First Order Evolution Equations
• Global Solvability of an Abstract Complex
• Remarks about global analytic hypoellipticity
• PERTURBATIONS OF VECTOR FIELDS ON TORI: RESONANT NORMAL FORMS AND DIOPHANTINE PHENOMENA
• Orbits of Families of Vector Fields and Integrability of Distributions
• Global Hypoellipticity and Liouville Numbers
• Solvability of a first order linear partial differential equation
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