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Zapiski Nauchnykh Seminarov POMI, 2014, Volume 425, Pages 35–45 (Mi znsl6019)  
This article is cited in 10 scientific papers (total in 11 papers)

On symmetry of the extremal in some embedding theorems

E. V. Mukoseevaa, A. I. Nazarovab

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
Full-text PDF (198 kB) Citations (11) English version article
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Abstract: We study the symmetry/asymmetry of functions providing sharp constants in the embedding theorems $\mathring W_2^r(-1,1)\hookrightarrow\mathring W_\infty^k(-1,1)$ for various $r$ and $k$. The sharp constants for all $r>k$ in the cases $k=4$ and $k=6$ are calculated explicitly as well.
Key words and phrases: sharp constants, embedding theorems, symmetry and asymmetry of extremals.
Received: 05.08.2014
English version:
Journal of Mathematical Sciences (New York), 2015, Volume 210, Issue 6, Pages 779–786
DOI: https://doi.org/10.1007/s10958-015-2589-9
Bibliographic databases:
Document Type: Article
UDC: 517
Language: Russian
Citation: E. V. Mukoseeva, A. I. Nazarov, “On symmetry of the extremal in some embedding theorems”, Boundary-value problems of mathematical physics and related problems of function theory. Part 44, Zap. Nauchn. Sem. POMI, 425, POMI, St. Petersburg, 2014, 35–45; J. Math. Sci. (N. Y.), 210:6 (2015), 779–786
Citation in format AMSBIB
\Bibitem{MukNaz14}
\by E.~V.~Mukoseeva, A.~I.~Nazarov
\paper On symmetry of the extremal in some embedding theorems
\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 35--45
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6019}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2015
\vol 210
\issue 6
\pages 779--786
\crossref{https://doi.org/10.1007/s10958-015-2589-9}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84944699227}
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  • https://www.mathnet.ru/eng/znsl6019
  • https://www.mathnet.ru/eng/znsl/v425/p35
    Erratum
    • Corrigendum
      E. V. Mukoseeva, A. I. Nazarov
      Zap. Nauchn. Sem. POMI, 2020, 489, 225
    This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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