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arXiv · 1501.07081

Regularity of electromagnetic fields in convex domains

N. Filonov·A. Prokhorov
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Abstract

In this paper the "strong" Maxwell operator defined on fields from the Sobolev space $W_2^1$, and the "weak" Maxwell operator defined on the natural domain are considered. It is shown that in a convex domain, and, more generally, in a domain, which is locally $(W_3^2 \cap W^1_\infty)$-diffeomorphic to convex one, the "strong" and the "weak" Maxwell operators coincide.

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N. Filonov, A. Prokhorov. 2015-02-06. Regularity of electromagnetic fields in convex domains. https://arxiv.org/abs/1501.07081

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