论文标题
具有混合边界条件的希尔伯特综合体 - 第3部分：Biharmonic复合物
Hilbert Complexes with Mixed Boundary Conditions -- Part 3: Biharmonic Complexes
论文作者
论文摘要
我们表明，在有界强的Lipschitz结构域上具有混合边界条件的Biharmonic Hilbert络合物封闭并紧凑。至关重要的结果是紧凑的嵌入，这些嵌入方式通过抽象参数使用功能分析以及特定的常规分解。还证明了更高的Sobolev订单结果。本文扩展了作者对De Rham和弹性的最新结果，并具有混合边界条件，Pauly和Zulehner在Biharmonic Hilbert Complex上具有空的或全边界条件的结果。
We show that the biharmonic Hilbert complex with mixed boundary conditions on bounded strong Lipschitz domains is closed and compact. The crucial results are compact embeddings which follow by abstract arguments using functional analysis together with particular regular decompositions. Higher Sobolev order results are also proved. This paper extends recent results of the authors on the de Rham and elasticity Hilbert complexes with mixed boundary conditions and results of Pauly and Zulehner on the biharmonic Hilbert complex with empty or full boundary conditions.
