弹性复合体：紧嵌入和正则分解
The Elasticity Complex: Compact Embeddings and Regular Decompositions
摘要：
本文研究了弹性力学中涉及对称张量场空间的Hilbert复形。对于所涉及的张量场和运营商，我们展示了封闭的范围，弗里德里希/庞加莱型估计，亥姆霍兹型分解，经常分解，经常的潜力，有限的上同调群，最重要的是，新的紧凑嵌入结果。我们的结果适用于任意拓扑的一般有界强Lipschitz域，并依赖于一般的泛函分析框架（FA-ToolBox）。此外，我们提出了一个简单的技术来证明紧嵌入的基础上定期分解/潜力和Rellich的截口定理，它可以很容易地适用于任何希尔伯特复杂。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
