Nonlocal Differential Equations in Analysis and Geometry

分析和几何中的非局部微分方程

• 批准号: 281530525
• 负责人: Professor Dr. Ernst Kuwert, since 9/2017
• 金额: --
• 依托单位: Department of Mathematics
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2016
• 资助国家: 德国
• 起止时间: 2015-12-31 至 2019-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/281530525?language=en
• 关键词: Nonlocal; Differential; Equations; Analysis; Geometry

As part of the application to the Heisenberg fellowship we study nonlocal, nonlinear PDE. We are interested in regularity results and singular sets (e.g. for fractional harmonic maps) and degenerate elliptic PDEs. As application we will consider problems from geomathematics, knot- and more general curvature energies, as well as geometric free boundary problems.

作为海森堡奖学金的应用程序的一部分，我们研究非局部，非线性偏微分方程。我们感兴趣的正则性结果和奇异集（例如分数调和映射）和退化椭圆偏微分方程。作为应用程序，我们将考虑问题，从geomathematics，结和更一般的曲率能量，以及几何自由边界问题。