某些矢量场的超微分周期解的存在性和正则性

IF 2.4 2区数学 Q1 MATHEMATICS

Journal of Differential Equations Pub Date : 2024-11-05 DOI:10.1016/j.jde.2024.10.042

Rafael B. Gonzalez

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引用次数: 0

摘要

我们考虑了一类作用于超微分周期函数空间的一阶偏微分算子，并利用算子系数的以下条件来描述它们的范围：某些子级集的连通性、系数虚部生成的子空间的维度以及 Diophantine 条件。此外，我们还证明了这些性质也与解的正则性有关。这些结果扩展了以前的 Gevrey 类结果。

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Existence and regularity of ultradifferentiable periodic solutions to certain vector fields

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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来源期刊

Journal of Differential Equations 数学-数学

CiteScore

4.40

自引率

8.30%

发文量

543

审稿时长

9 months

期刊介绍： The Journal of Differential Equations is concerned with the theory and the application of differential equations. The articles published are addressed not only to mathematicians but also to those engineers, physicists, and other scientists for whom differential equations are valuable research tools. Research Areas Include: • Mathematical control theory • Ordinary differential equations • Partial differential equations • Stochastic differential equations • Topological dynamics • Related topics