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既出现在几何和弹性中。在这个项目中，我们考虑了具有临界缩放的能量，特别是Willmore在空间表面的功能，以及Riemannian歧管之间地图的Biharmonic Energy。对于相关的梯度流以及对于固定溶液的序列，由于能量浓度引起的奇异性是可能的。我们有兴趣了解奇点的形成，以及找到自然条件之类的能量界限，以保证规律性。 Die Angabe des Links Ist Ausreichend。