Well-posedness of Kolmogorov-Fokker-Planck equations with unbounded drift

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-09-27 DOI:10.1016/j.jmaa.2024.128909

Francesca Anceschi , Giacomo Ascione , Daniele Castorina , Francesco Solombrino

引用次数: 0

Abstract

We consider Kolmogorov-Fokker-Planck equations with unbounded drift terms which are only measurable in time and locally Hölder continuous in space. In particular, we extend the parametrix method to this setting and we prove existence and uniqueness of measure solutions to the associated Cauchy problem, as well as the equivalence with the corresponding stochastic formulation.

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具有无约束漂移的科尔莫戈罗夫-福克-普朗克方程的好求性

我们考虑了带有无约束漂移项的科尔莫格罗夫-福克-普朗克方程，这些漂移项在时间上是可测量的，在空间上是局部荷尔德连续的。特别是，我们将参数矩阵法扩展到这一设置，并证明了相关考希问题的量解的存在性和唯一性，以及与相应随机公式的等价性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.