从复合物中复合
Complexes from complexes
摘要：
本文讨论了由微分方程中的各种问题所产生的微分复形的导出及其性质，并在连续介质力学、相对论和其他领域中得到应用。我们提出了一个系统的程序，从众所周知的微分复杂，如德拉姆复杂，推导出新的复合物，并推导出新的复合物的性质从旧的。我们与输出复形的上同调的输入复形，并表明，新的复杂的封闭范围，因此，满足霍奇分解，庞加莱型不等式，适定的Hodge-Laplacian边值问题，经常分解，一般Lipschitz域上的紧性。
英文摘要：
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.
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。
