Global \(s\)-solvability and global \(s\)-hypoellipticity for certain perturbations of zero order of systems of constant real vector fields

DOI10.1016/j.jde.2008.02.020zbMath1155.35010OpenAlexW2059747877MaRDI QIDQ926870

Gerson Petronilho, Sérgio Luís Zani

Publication date: 21 May 2008

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2008.02.020

zbMATH Keywords

Gevrey classes

Mathematics Subject Classification ID

Pseudodifferential operators as generalizations of partial differential operators (35S05) Hypoelliptic equations (35H10)

Related Items (9)

Global Solvability in Functional Spaces for Smooth Nonsingular Vector Fields in the Plane ⋮ Partial Fourier series on compact Lie groups ⋮ Global Gevrey hypoellipticity on the torus for a class of systems of complex vector fields ⋮ Perturbations by lower order terms do not destroy the global hypoellipticity of certain systems of pseudodifferential operators defined on torus ⋮ Solvability for perturbations of a class of real vector fields on the two-torus ⋮ Global Gevrey solvability for a class of perturbations of involutive systems ⋮ Global hypoellipticity and global solvability for vector fields on compact Lie groups ⋮ Fourier analysis for Denjoy–Carleman classes on the torus ⋮ Global properties of vector fields on compact Lie groups in Komatsu classes

Cites Work

• Unnamed Item
• Unnamed Item
• Global \(s\)-solvability, global \(s\)-hypoellipticity and Diophantine phenomena
• Global solvability and simultaneously approximable vectors
• An example of a globally hypoelliptic operator
• Regularity of a class of subLaplacians on the 3-dimensional torus
• Solvability in the large for a class of vector fields on the torus
• The global hypoellipticity of a class of degenerate elliptic-parabolic operators
• On the solvability of linear partial differential equations in spaces of hyperfunctions
• Conditions necessaires d'hypoanalyticite pour des opérateurs invariants à gauche homogenes sur un groupe nilpotent gradue
• Some note on Gevrey hypoellipticity and solvability on torus
• Global solvability and hypoellipticity on the torus for a class of differential operators with variable coefficients
• Global solvability on the torus for certain classes of operators in the form of a sum of squares of vector fields
• Closedness of the range for vector fields on the torus
• On global hypoellipticity of degenerate elliptic operators
• Perturbations of globally hypoelliptic operators
• Propagation of regularity and global hypoellipticity
• Global solvability on the torus for certain classes of formally self-adjoint operators
• On the Gevrey hypo-ellipticity of sums of squares of vector fields.
• Global properties of a class of overdetermined systems.
• Global hypoellipticity and global solvability in Gevrey classes on the \(n\)-dimensional torus
• On the global solvability in Gevrey classes on the \(n\)-dimensional torus
• Global analytic hypoellipticity of a class of degenerate elliptic operators on the torus
• Global analytic hypoellipticity in the presence of symmetry
• WKB analysis to global solvability and hypoellipticity
• On degenerate elliptic operators of infinite type
• Global hypoellipticity and simultaneous approximability
• Simultaneous reduction of a family of commuting real vector fields and global hypoellipticity
• Global analytic and Gevrey hypoellipticity of sublaplacians under Diophantine conditions
• Global Solvability for a Class of Complex Vector Fields on the Two-Torus
• On 𝐶^{∞} and Gevrey regularity of sublaplacians
• On the Fourier Analysis of Operators on the Torus
• Globally Hypoelliptic and Globally Solvable First Order Evolution Equations
• Global Solvability of an Abstract Complex
• Global analytic regularity for sums of squares of vector fields
• Remarks about global analytic hypoellipticity
• PERTURBATIONS OF VECTOR FIELDS ON TORI: RESONANT NORMAL FORMS AND DIOPHANTINE PHENOMENA
• Global (and local) analyticity for second order operators constructed from rigid vector fields on products of tori
• Hypoelliptic vector fields and almost periodic motions on the torus Tⁿ
• Prescribing analytic singularities for solutions of a class of vector fields on the torus
• Global Hypoellipticity and Liouville Numbers
• Global solvability for certain classes of underdetermined systems of vector fields

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