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Existence and Regularity of Periodic Solutions to Certain First-Order Partial Differential Equations

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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,… Click to show full abstract

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.

Keywords: periodic solutions; certain first; regularity periodic; solutions certain; existence regularity

Journal Title: Journal of Fourier Analysis and Applications
Year Published: 2017

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