Weck 选择定理：任意维弱 Lipschitz 有界混合边界域上的 Maxwell 紧性性质
偏微分方程分析
2019-05-01 v4 数学物理
math.MP
摘要
证明了具有弱外微分与余导数的微分形式空间紧嵌入到平方可积微分形式空间中。考虑了弱 Lipschitz 域上的混合边界条件。此外，证明了诸如 Maxwell 估计、Helmholtz 分解和静态解理论等典型应用。作为证明的副产品与关键工具，我们也展示了正则势与正则分解的存在性。
引用
@article{arxiv.1809.01192,
title = {Weck's Selection Theorem: The Maxwell Compactness Property for Bounded Weak Lipschitz Domains with Mixed Boundary Conditions in Arbitrary Dimensions},
author = {Sebastian Bauer and Dirk Pauly and Michael Schomburg},
journal= {arXiv preprint arXiv:1809.01192},
year = {2019}
}
备注
key words: Maxwell compactness property, weak Lipschitz domain, Maxwell estimate, Helmholtz decomposition, electro-magneto statics, mixed boundary conditions, vector potentials. arXiv admin note: text overlap with arXiv:1511.06697