Weck's Selection Theorem: The Maxwell Compactness Property for Bounded Weak Lipschitz Domains with Mixed Boundary Conditions in Arbitrary Dimensions
Analysis of PDEs
2019-05-01 v4 Mathematical Physics
math.MP
Abstract
It is proved that the space of differential forms with weak exterior and co-derivative, is compactly embedded into the space of square integrable differential forms. Mixed boundary conditions on weak Lipschitz domains are considered. Furthermore, canonical applications such as Maxwell estimates, Helmholtz decompositions and a static solution theory are proved. As a side product and crucial tool for our proofs we show the existence of regular potentials and regular decompositions as well.
Keywords
Cite
@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}
}
Comments
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