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Existence and regularity of periodic solutions to certain first-order partial differential equations. (English) Zbl 1357.35020
Summary: We present conditions on the coefficients of a class of vector fields on the torus which yield a characterization of global solvability as well as global hypoellipticity, in other words, the existence and regularity of periodic solutions. Diophantine conditions and connectedness of certain sublevel sets appear in a natural way in our results.

MSC:
35B10 Periodic solutions to PDEs
35A01 Existence problems for PDEs: global existence, local existence, non-existence
35H10 Hypoelliptic equations
35B65 Smoothness and regularity of solutions to PDEs
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