Global hypoellipticity, global solvability and normal form for a class of real vector fields on a torus and application

DOI10.1090/S0002-9947-2011-05359-6zbMath1235.35010OpenAlexW1993393444MaRDI QIDQ3103845

Gerson Petronilho

Publication date: 12 December 2011

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-2011-05359-6

zbMATH Keywords

vector fieldnormal formglobal solvabilityglobal hypoellipticity

Mathematics Subject Classification ID

Linear first-order PDEs (35F05) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Hypoelliptic equations (35H10)

Related Items (15)

Global hypoellipticity for first-order operators on closed smooth manifolds ⋮ Partial Fourier series on compact Lie groups ⋮ Перiодичнi розв’язки у просторi Соболєва для рiвняння iз частинними похiдними, коефiцiєнти якого залежать вiд параметра ⋮ Globally hypoelliptic triangularizable systems of periodic pseudo‐differential operators ⋮ Cohomology relative to a system of closed forms on the torus ⋮ Global solvability and propagation of regularity of sums of squares on compact manifolds ⋮ Global properties of vector fields on compact Lie groups in Komatsu classes. II: Normal forms ⋮ Laplacians on smooth distributions ⋮ Global hypoellipticity and global solvability for vector fields on compact Lie groups ⋮ Global hypoellipticity for a class of pseudo-differential operators on the torus ⋮ Global hypoellipticity for a class of periodic Cauchy operators ⋮ Global analytic hypoellipticity for a class of evolution operators on \(\mathbb{T}^1 \times \mathbb{S}^3\) ⋮ 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

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