Elliptic systems of higher order with critical nonlinearity

具有临界非线性的高阶椭圆系统

• 批准号: 262992434
• 负责人: Professor Dr. Andreas Gastel
• 金额: --
• 依托单位: Fachgebiet Geometrische 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/262992434?language=en
• 关键词: Elliptic; systems; higher; order; critical

The regularity theory for weak solutions of quasilinear elliptic systems of second or fourth order with critical nonlinearity has been pushed to new levels in recent work by Rivière, Struwe, and Lamm. A similarly general theory for systems of higher order (in divergence form) is still lacking. In our project, we would like to start it with considering the problem in the critical dimension. This will probably involve the methods mentioned, combined with arguments which allow handling the Sobolev spaces of negative differentiability that are expected to occur.

具有临界非线性项的二阶或四阶拟线性椭圆型方程组弱解的正则性理论在最近的工作中被Rivière，Struwe和Lamm推向了新的水平.对于高阶系统（发散形式），仍然缺乏类似的一般理论。在我们的项目中，我们希望从考虑关键维度的问题开始。这将可能涉及的方法提到，结合参数，允许处理索伯列夫空间的负微分，预计将发生。

项目成果

Regularität der Lösungen von Systeme (2m)-ter Ordnung vom polyharmonischen Typ in kritischer Dimension

临界维数(2m)阶多调和型系统解的正则性

• DOI: 10.17185/duepublico/70153
• 发表时间: 2019
• 作者: Frédéric Louis de Longueville