Second order variational integrals with critical scaling

具有临界标度的二阶变分积分

• 批准号: 5363153
• 负责人: Professor Dr. Ernst Kuwert
• 金额: --
• 依托单位: Abteilung für Reine Mathematik
• 依托单位国家: 德国
• 项目类别: Research Units
• 财政年份: 2002
• 资助国家: 德国
• 起止时间: 2001-12-31 至 2010-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/5363153?language=en
• 关键词: Second; order; variational; integrals; critical

Variational integrals involving second order derivatives occur both in geometry and in elasticity. In this project we consider energies with critical scaling, in particular the Willmore functional for surfaces in space and the biharmonic energy for maps between Riemannian manifolds. For the associated gradient flows and also for sequences of stationary solutions, singularities due to energy concentrations are possible. We are interested in understanding the formation of the singularities, and in finding natural conditions like energy bounds which guarantee regularity.http://home.mathematik.uni-freiburg.de/fg/projects/A2/Der Text der Zusammenfassung ist der oben angegebenen Seite zu entnehmen. Die Angabe des Links ist ausreichend.

涉及二阶导数的变分积分在几何学和弹性力学中都有出现。在这个项目中，我们考虑的能量与临界标度，特别是Willmore功能的表面在空间和双调和能量之间的映射黎曼流形。对于相关的梯度流和稳态解的序列，由于能量集中而产生的奇异性是可能的。我们感兴趣的是理解奇点的形成，并寻找自然条件，如能量界限，以保证。regularity.http://home.mathematik.uni-freiburg.de/fg/projects/A2/Der链接的角度是正确的。