Existence and regularity of ultradifferentiable periodic solutions to certain vector fields

2023/12/06 by Rafael B. Gonzalez, Gonzalez, Rafael B.
Computer Science · Mathematics · #35A01 #35B10 #35H10 #Advanced Differential Equations and Dynamical Systems #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis

paper · pdf · doi:10.48550/arxiv.2312.03822

openalex publication_date 2023/12/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a class of first-order partial differential operators, acting on the space of ultradifferentiable periodic functions, and we describe their range by using the following conditions on the coefficients of the operators: the connectedness of certain sublevel sets, the dimension of the subspace generated by the imaginary part of the coefficients, and Diophantine conditions. In addition, we show that these properties are also linked to the regularity of the solutions. The results extend previous ones in Gevrey classes.

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