Applications of a version of the de Rham lemma to the existence theory of a weak solution to the Maxwell–Stokes type equation

In this paper, we show the existence of a weak solution to the Maxwell–Stokes type equation with a potential satisfying the Dirichlet condition, under the hypothesis that the domain has no holes, using a version of the de Rham lemma that was proved in our previous paper. We also give the regularity...

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Bibliographic Details
Published inArabian Journal of Mathematics Vol. 9; no. 1; pp. 9 - 18
Main Author Aramaki, Junichi
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Science and Business Media LLC 01.04.2020
Springer Berlin Heidelberg
Springer
Springer Nature B.V
Subjects
Bars (Drinking establishments)
Dirichlet problem
Mathematics
Mathematics and Statistics
35D05
35A05
35J50
35A15
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Summary:In this paper, we show the existence of a weak solution to the Maxwell–Stokes type equation with a potential satisfying the Dirichlet condition, under the hypothesis that the domain has no holes, using a version of the de Rham lemma that was proved in our previous paper. We also give the regularity of weak solutions.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:2193-5343
2193-5351
2193-5351
DOI:10.1007/s40065-018-0224-6