Global Solvability for a Class of Complex Vector Fields on the Two-Torus

DOI10.1081/PDE-120037332zbMath1065.35088OpenAlexW2044315909MaRDI QIDQ3157909

Gerson Petronilho, Paulo D. Cordaro, Adalberto Panobianco Bergamasco

Publication date: 20 January 2005

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1081/pde-120037332

zbMATH Keywords

condition (P) of Nirenberg and Treves

Mathematics Subject Classification ID

Related Items (30)

Solvability in the large for a class of vector fields on the torus ⋮ Global hypoellipticity for first-order operators on closed smooth manifolds ⋮ Partial Fourier series on compact Lie groups ⋮ Globally hypoelliptic triangularizable systems of periodic pseudo‐differential operators ⋮ Solvability of a first order differential operator on the two-torus ⋮ Global solvability and global hypoellipticity in Gevrey classes for vector fields on the torus ⋮ Solvability for perturbations of a class of real vector fields on the two-torus ⋮ Global solvability of real analytic complex vector fields in two variables ⋮ \(C^k\)-solvability near the characteristic set for a class of planar complex vector fields of infinite type ⋮ Global hypoellipticity and global solvability for vector fields on compact Lie groups ⋮ Global \(s\)-solvability and global \(s\)-hypoellipticity for certain perturbations of zero order of systems of constant real vector fields ⋮ Global solvability for a class of overdetermined systems ⋮ Global solvability and global hypoellipticity for a class of complex vector fields on the 3-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 ⋮ Solvability near the characteristic set for a class of planar vector fields of infinite type. ⋮ Existence of global solutions for a class of vector fields on the three-dimensional torus ⋮ Global hypoellipticity for a class of periodic Cauchy operators ⋮ Solvability of a class of first order differential operators on the torus ⋮ Fourier analysis for Denjoy–Carleman classes on the torus ⋮ Gevrey solvability near the characteristic set for a class of planar complex vector fields of infinite type ⋮ Nonexistence of global solutions for a class of complex vector fields on two-torus ⋮ Elliptic planar vector fields with degeneracies ⋮ Solvability in the large for a class of complex vector fields on the cylinder ⋮ Solvability near the characteristic set for a special class of complex vector fields ⋮ Properties of solutions of a class of planar elliptic operators with degeneracies ⋮ Global hypoellipticity, global solvability and normal form for a class of real vector fields on a torus and application ⋮ Global properties of vector fields on compact Lie groups in Komatsu classes ⋮ Global solvability and global hypoellipticity of complex vector fields on surfaces

Cites Work

• Addition de variables et application à la régularité
• Propagation des singularités pour les opérateurs différentiels de type principal, localement résolubles, à coefficients analytiques, en dimension 2
• Propagation of singularities and semi-global existence theorems for (pseudo-)differential operators of principal type
• Orbits and global unique continuation for systems of vector fields
• Closedness of the range for vector fields on the torus
• On local solvability of linear partial differential equations—part II. Sufficient conditions
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