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Zapiski Nauchnykh Seminarov POMI, 2016, Volume 444, Pages 133–156 (Mi znsl6273)  
This article is cited in 1 scientific paper (total in 1 paper)

Proof of Schauder estimates for parabolic initial-boundary value model problems via O. A. Ladyzhenskaya's Fourier multipliers theorem

V. A. Solonnikov

St. Petersburg Department of Steklov Mathematical Institute, Fontanka 27, 191023 St. Petersburg, Russia
Full-text PDF (292 kB) Citations (1)
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Abstract: The paper is concerned with estimates of the Hölder norms of solutions of model parabolic initial-boundary value problems in a half-space. The proof is based on the theorem on the Fourier multipliers in anisotropic Hölder spaces due to O. A. Ladyzhenskaya and on K. K. Golovkin's theorem on equivalent norms in these spaces.
Key words and phrases: Fourier multipliers, Schauder estimates, parabolic problems.
Funding agency Grant number
Russian Foundation for Basic Research 14-01-00306a
The work is supported by the RFBR grant 14-01-00306a.
Received: 24.03.2016
English version:
Journal of Mathematical Sciences (New York), 2017, Volume 224, Issue 3, Pages 475–491
DOI: https://doi.org/10.1007/s10958-017-3430-4
Bibliographic databases:
Document Type: Article
UDC: 517
Language: English
Citation: V. A. Solonnikov, “Proof of Schauder estimates for parabolic initial-boundary value model problems via O. A. Ladyzhenskaya's Fourier multipliers theorem”, Boundary-value problems of mathematical physics and related problems of function theory. Part 45, Zap. Nauchn. Sem. POMI, 444, POMI, St. Petersburg, 2016, 133–156; J. Math. Sci. (N. Y.), 224:3 (2017), 475–491
Citation in format AMSBIB
\Bibitem{Sol16}
\by V.~A.~Solonnikov
\paper Proof of Schauder estimates for parabolic initial-boundary value model problems via O.\,A.~Ladyzhenskaya's Fourier multipliers theorem
\inbook Boundary-value problems of mathematical physics and related problems of function theory. Part~45
\serial Zap. Nauchn. Sem. POMI
\yr 2016
\vol 444
\pages 133--156
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6273}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3509682}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2017
\vol 224
\issue 3
\pages 475--491
\crossref{https://doi.org/10.1007/s10958-017-3430-4}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85020206149}
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  • https://www.mathnet.ru/eng/znsl/v444/p133
    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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