论文标题
复合物的复合物
Complexes from complexes
论文作者
论文摘要
本文涉及由微分方程中的各种问题以及连续力学，相对性和其他领域的应用引起的差分复合物的推导和特性。我们提出了一个系统的过程，该程序从诸如DE RHAM复合物等易于理解的差分复合物开始，从旧配合物中得出了新的配合物并推论了新综合体的特性。我们将输出复合物的共同论与输入复合物的共同体相关联，并表明新复合物已关闭范围，因此满足了Hodge分解，庞加莱型不平等，霍奇 - 拉平质边界价值问题，常规的分解，常规的分解和对一般Lipschitz域上的紧凑型。
This paper is concerned with the derivation and properties of differential complexes arising from a variety of problems in differential equations, with applications in continuum mechanics, relativity, and other fields. We present a systematic procedure which, starting from well-understood differential complexes such as the de Rham complex, derives new complexes and deduces the properties of the new complexes from the old. We relate the cohomology of the output complex to that of the input complexes and show that the new complex has closed ranges, and, consequently, satisfies a Hodge decomposition, Poincaré type inequalities, well-posed Hodge-Laplacian boundary value problems, regular decomposition, and compactness properties on general Lipschitz domains.
