Regularity of electromagnetic fields in convex domains

TL;DR

This paper investigates the conditions under which the 'strong' and 'weak' Maxwell operators are equivalent in convex and certain diffeomorphic domains, advancing the mathematical understanding of electromagnetic field regularity.

Contribution

It establishes the equivalence of 'strong' and 'weak' Maxwell operators in convex domains and those locally diffeomorphic to convex domains, extending previous results.

Findings

'Strong' and 'weak' Maxwell operators coincide in convex domains.

Equivalence extends to domains locally diffeomorphic to convex ones.

Results improve mathematical foundations for electromagnetic field analysis.

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.