Traces of differential forms on Lipschitz domains, the boundary De Rham complex, and Hodge decompositions
Traces of differential forms on Lipschitz domains, the boundary De Rham complex, and Hodge decompositions
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Lipschitz 域、边界 De Rham 复合体和 Hodge 分解上的微分形式迹
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
Mei
中科院分区：
文献类型：
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作者：
D. Mitrea;M. Mitrea;Mei
本文研究了经典的标值函数迹和扩张定理在何种程度上可以推广到高阶微分形式。为了最大的适用性，这是在黎曼流形的Lipschitz子域的上下文中完成的，并且在Besov和Triebel-Lizorkin空间的尺度上。在这方面的一个关键因素是边界德拉姆复杂，我们认为在上述几何和分析设置。Hodge分解和插值约束的应用程序也被提出。
We study the extent to which classical trace and extension theorems for scalar-valued functions can be extended to differential forms of higher-degree. For maximum applicability, this is done in the context of Lipschitz subdomains of Riemannian manifolds, and on the scale of Besov and Triebel-Lizorkin spaces. A key ingredient in this regard is the boundary De Rham complex, which we consider in the geometric and analytic setting above. Applications to Hodge-decompositions and interpolation with constraints are also presented.