RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Zap. Nauchn. Sem. POMI:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Zap. Nauchn. Sem. POMI, 2014, Volume 425, Pages 55–85 (Mi znsl6021)  

This article is cited in 2 scientific papers (total in 2 papers)

Regularity of electromagnetic fields in convex domains

A. Prohorova, N. Filonovab

a St. Petersburg State University, St. Petersburg, Russia
b St. Petersburg Department of V. A. Steklov Institute of Mathematics of the Russian Academy of Sciences, St. Petersburg, Russia

Abstract: The “strong” Maxwell operator defined on the 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 the convex domains, and more generally, in the domains which are locally $(W^2_3\cap W^1_\infty)$-diffeomorphic to convex ones, the “strong” and the “weak” Maxwell operators coincide.

Key words and phrases: domain of the Maxwell operator, convex domains, exterior ball condition.

Full text: PDF file (327 kB)
References: PDF file   HTML file

English version:
Journal of Mathematical Sciences (New York), 2015, 210:6, 793–813

UDC: 517
Received: 28.08.2014

Citation: A. Prohorov, N. Filonov, “Regularity of electromagnetic fields in convex domains”, Boundary-value problems of mathematical physics and related problems of function theory. Part 44, Zap. Nauchn. Sem. POMI, 425, POMI, St. Petersburg, 2014, 55–85; J. Math. Sci. (N. Y.), 210:6 (2015), 793–813

Citation in format AMSBIB
\Bibitem{ProFil14}
\by A.~Prohorov, N.~Filonov
\paper Regularity of electromagnetic fields in convex domains
\inbook Boundary-value problems of mathematical physics and related problems of function theory. Part~44
\serial Zap. Nauchn. Sem. POMI
\yr 2014
\vol 425
\pages 55--85
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6021}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2015
\vol 210
\issue 6
\pages 793--813
\crossref{https://doi.org/10.1007/s10958-015-2591-2}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84959853995}


Linking options:
  • http://mi.mathnet.ru/eng/znsl6021
  • http://mi.mathnet.ru/eng/znsl/v425/p55

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. O. Prokhorov, N. D. Filonov, “Operator Maksvella s periodicheskimi koeffitsientami v tsilindre”, Algebra i analiz, 29:6 (2017), 182–196  mathnet  elib
    2. G. S. Alberti, “Holder regularity for Maxwell's equations under minimal assumptions on the coefficients”, Calc. Var. Partial Differ. Equ., 57:3 (2018), 71  crossref  mathscinet  zmath  isi  scopus
  • Записки научных семинаров ПОМИ
    Number of views:
    This page:179
    Full text:87
    References:31

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020