Regularity of Evolutionary Problems via Harmonic Analysis and Operator Theory

通过调和分析和算子理论研究演化问题的规律性

• 批准号: 263969954
• 负责人: Professor Dr. Wolfgang Arendt
• 金额: --
• 依托单位: Institut für Angewandte Analysis
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2014
• 资助国家: 德国
• 起止时间: 2013-12-31 至 2017-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/263969954?language=en
• 关键词: Regularity; Evolutionary; Problems; via; Harmonic

The proposal consists of four closely related parts. A first project concerns operator-valued Fourier multipliers. Here the proof of the Marcinkiewicz (periodic case) and Mikhlin Multiplier Theorem on spaces with Muckenhoupt weights form our central goal. Further aims concern multipliers with respect to general Schauder decompositions with applications to the closedness-of-the-sum-problem. The second part is the development of a structure theory for maximal regularity where positivity plays an essential role. Wide open is still maximal regularity in the non-autonomous case to which the third part is devoted. It is strongly motivated by quasilinear parabolic problems. Finally, all results will be tested for elliptic operators with diverse boundary conditions, the last part of the proposal.

该提案由四个密切相关的部分组成。第一个项目涉及算子值傅立叶乘法器。在这里，Marcinkiewicz（周期情况）和米克林乘子定理的证明与Muckenhoupt权重空间形成我们的中心目标。进一步的目标关注乘数与一般Schauder分解与应用的封闭性的总和问题。第二部分是积极性在最大规律性结构理论中的发展。在第三部分讨论的非自治情形中，大开仍然是最大正则性。它是由拟线性抛物问题强烈的动机。最后，所有的结果将被测试的椭圆算子与不同的边界条件，建议的最后一部分。

项目成果

J.-L. Lions' Problem Concerning Maximal Regularity of Equations Governed by Non-Autonomous Forms

J-L Lions 关于非自治形式控制方程的最大正则性问题

• DOI: 10.1016/j.anihpc.2016.05.001
• 发表时间: 2017
• 期刊: arXiv: Functional Analysis
• 作者: S. Fackler

J. L. Lions’ problem on maximal regularity

J L Lions关于最大正则性问题

• DOI: 10.1007/s00013-017-1031-6
• 发表时间: 2017
• 期刊: Archiv der Mathematik
• 影响因子: 0.6
• 作者: W. Arendt;S. Fackler;D. Dier
• 通讯作者: D. Dier

Non-Autonomous Maximal Regularity for Forms Given by Elliptic Operators of Bounded Variation

有界变分椭圆算子给出的形式的非自治最大正则性

• DOI: 10.1016/j.jde.2017.04.036
• 发表时间: 2017
• 期刊: arXiv: Functional Analysis
• 作者: S. Fackler

Nonautonomous maximal Lp-regularity under fractional Sobolev regularity in time

时间上分数 Sobolev 正则性下的非自主最大 Lp 正则性

• DOI: 10.2140/apde.2018.11.1143
• 发表时间: 2018
• 期刊: Analysis & PDE
• 影响因子: 2.2
• 作者: S. Fackler