{"title":"在Young和粗糙微分方程的Besov设置中Lipschitz估计","authors":"Peter K. Friz , Hannes Kern , Pavel Zorin-Kranich","doi":"10.1016/j.jde.2025.113507","DOIUrl":null,"url":null,"abstract":"<div><div>We develop a set of techniques that enable us to effectively recover Besov rough analysis from <em>p</em>-variation rough analysis. Central to our approach are new metric groups, in which some objects in rough path theory that have been previously viewed as two-parameter can be considered as path increments. Furthermore, we develop highly precise Lipschitz estimates for Young and rough differential equations, both in the variation and Besov scale.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"443 ","pages":"Article 113507"},"PeriodicalIF":2.3000,"publicationDate":"2025-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Lipschitz estimates in the Besov settings for Young and rough differential equations\",\"authors\":\"Peter K. Friz , Hannes Kern , Pavel Zorin-Kranich\",\"doi\":\"10.1016/j.jde.2025.113507\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>We develop a set of techniques that enable us to effectively recover Besov rough analysis from <em>p</em>-variation rough analysis. Central to our approach are new metric groups, in which some objects in rough path theory that have been previously viewed as two-parameter can be considered as path increments. Furthermore, we develop highly precise Lipschitz estimates for Young and rough differential equations, both in the variation and Besov scale.</div></div>\",\"PeriodicalId\":15623,\"journal\":{\"name\":\"Journal of Differential Equations\",\"volume\":\"443 \",\"pages\":\"Article 113507\"},\"PeriodicalIF\":2.3000,\"publicationDate\":\"2025-06-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Differential Equations\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0022039625005340\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022039625005340","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Lipschitz estimates in the Besov settings for Young and rough differential equations
We develop a set of techniques that enable us to effectively recover Besov rough analysis from p-variation rough analysis. Central to our approach are new metric groups, in which some objects in rough path theory that have been previously viewed as two-parameter can be considered as path increments. Furthermore, we develop highly precise Lipschitz estimates for Young and rough differential equations, both in the variation and Besov scale.
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