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

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• 作者：Adalberto P. Bergamasco…
• 关键词：Global solvability ; Global hypoellipticity ; Vector fields ; Periodic solutions ; Fourier series
• 刊名：Journal of Fourier Analysis and Applications
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：23
• 期：1
• 页码：65-90
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Fourier Analysis; Signal,Image and Speech Processing; Abstract Harmonic Analysis; Approximations and Expansions; Partial Differential Equations; Mathematical Methods in Physics;
• 出版者：Springer US
• ISSN：1531-5851
• 卷排序：23

文摘

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.