Ordinary differential equations with rough coefficients and the renormalization theorem of Ambrosio [after Ambrosio, DiPerna, Lions]

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2008-01-01 DOI:10.5167/UZH-21441

Camillo De Lellis

引用次数: 12

Abstract

In a seminal paper of almost 20 years ago, R.J. DiPerna and P.-L. Lions initiated the theory of renormalized solutions to study the well-posedness of Ordinary Differential Equations and Transport Equations with discontinuous coefficients. In a recent work L. Ambrosio solved the long-standing open problem of extending this theory to BV coefficients, the most common functional-analytic closure of classical functions with jump discontinuities. Besides its intrinsic interest, Ambrosio's Theorem has been used to solve relevant problems in Partial Differential Equations and it opened the way to a series of new questions.

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粗糙系数常微分方程与Ambrosio的重整化定理[源自Ambrosio, DiPerna, Lions]

在近20年前的一篇开创性论文中，R.J.迪珀纳和p.l。狮子开创了重整化解理论，以研究具有不连续系数的常微分方程和输运方程的适定性。在最近的工作中，L. Ambrosio解决了将该理论扩展到BV系数的长期开放问题，BV系数是具有跳跃不连续的经典函数的最常见的泛函解析闭包。安布罗西奥定理除了其固有的兴趣外，还被用于解决偏微分方程中的相关问题，并为一系列新问题开辟了道路。

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.