On the local solvability and the local integrability of systems of vector fields

DOI10.1007/BF02393203zbMath0534.35009OpenAlexW2054558106MaRDI QIDQ790339

François Treves

Publication date: 1983

Published in: Acta Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02393203

zbMATH Keywords

Cauchy problemlocal solvabilitylocal integrabilityFrobenius conditionsystems of vector fields

Mathematics Subject Classification ID

Linear first-order PDEs (35F05) Overdetermined systems of PDEs with variable coefficients (35N10)

Related Items (25)

Keeping track of limit cycles ⋮ On the local solvability of certain overdetermined systems of first-order linear PDE ⋮ Real-analytic solvability for differential complexes associated to locally integrable structures ⋮ Necessary and sufficient conditions for the local solvability in hyperfunctions of a class of systems of complex vector fields ⋮ Local solvability of analytic pseudodifferential complexes in top degree ⋮ Homology and cohomology in hypo-analytic structures of the hypersurfaces type ⋮ Local Integrability of Mizohata Structures ⋮ Global solvability of real analytic involutive systems on compact manifolds ⋮ On the range of unsolvable systems induced by complex vector fields ⋮ Hypoellipticity for certain systems of complex vector fields ⋮ A FOURIER-TYPE CHARACTERISATION FOR GEVREY VECTORS ON HYPO-ANALYTIC STRUCTURES AND PROPAGATION OF GEVREY SINGULARITIES ⋮ Local exactness in a class of differential complexes ⋮ Local solvability in \(C^{\infty}_ c\) of over-determined systems of vector fields ⋮ Local solvability in a class of overdetermined systems of linear PDE ⋮ Hölder-Łojasiewicz inequalities for volumes of tame objects ⋮ A Kernel Approach to the Local Solvability of the Tangential Cauchy Riemann Equations ⋮ On the range of the lewy complex ⋮ Local solvability for real-analytic involutive structures of tube type of corank one ⋮ Almost Mizohata Operators ⋮ A vanishing theorem for a class of systems with simple characteristics ⋮ Local solvability for a class of differential complexes ⋮ On the triangulation of subanalytic morphisms. ⋮ On the local solvability and the local integrability of systems of vector fields ⋮ The Mizohata complex ⋮ Topological invariance of the solvability of complex-valued vector fields in the plane

Cites Work

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• On the local solvability and the local integrability of systems of vector fields
• Stratification of real analytic mappings and images
• Triangulation of subanalytic sets and proper subanalytic maps
• Semi-Algebraic Local-Triviality in Semi-Algebraic Mappings
• Triangulation of Stratified Objects

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