论文标题
弹性复合物：紧凑的嵌入和常规分解
The Elasticity Complex: Compact Embeddings and Regular Decompositions
论文作者
论文摘要
我们研究了涉及对称张量场空间的弹性的希尔伯特综合体。对于相关的张量场和操作员，我们显示了封闭的范围，弗里德里奇/庞加罗型估计值，helmholtz型分解，常规分解，常规电位，有限的共同体学组，以及最重要的是，新的紧凑型嵌入结果。我们的结果适用于任意拓扑的一般强大Lipschitz领域，并依靠一般功能分析框架（FA-Toolbox）。此外，我们提出了一种简单的技术，可以根据常规分解/电位证明紧凑的嵌入以及Rellich的部分定理，可以很容易地适应任何Hilbert Complex。
We investigate the Hilbert complex of elasticity involving spaces of symmetric tensor fields. For the involved tensor fields and operators we show closed ranges, Friedrichs/Poincare type estimates, Helmholtz type decompositions, regular decompositions, regular potentials, finite cohomology groups, and, most importantly, new compact embedding results. Our results hold for general bounded strong Lipschitz domains of arbitrary topology and rely on a general functional analysis framework (FA-ToolBox). Moreover, we present a simple technique to prove the compact embeddings based on regular decompositions/potentials and Rellich's section theorem, which can be easily adapted to any Hilbert complex.
