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Zapiski Nauchnykh Seminarov POMI, 2000, Volume 269, Pages 322–338 (Mi znsl1322)  
This article is cited in 8 scientific papers (total in 8 papers)

One-dimensional parabolic problem arising in the study of some free boundary problems

V. A. Solonnikova, A. Fasanob

a St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
b Università degli Studi di Firenze
Full-text PDF (227 kB) Citations (8)
Abstract: The paper is concerned with one-dimensional parabolic problem in the domain bounded by straight lines $x=0$ and $x=kt$, $k>0$, $(x,t)\in\mathbb R^2$, with the Neumann boundary condition on the line $x=0$ and with dynamic boundary condition on the lne $x=kt$. For the solution of this problem coercive estimate in a weighted Hölder norm is obtained. It is shown that this estimate can be useful for the analysis of parabolic free boundary problems.
Received: 11.09.1999
English version:
Journal of Mathematical Sciences (New York), 2003, Volume 115, Issue 1, Pages 2066–2075
DOI: https://doi.org/10.1023/A:1022616300191
Bibliographic databases:
UDC: 517.9
Language: Russian
Citation: V. A. Solonnikov, A. Fasano, “One-dimensional parabolic problem arising in the study of some free boundary problems”, Questions of quantum field theory and statistical physics. Part 16, Zap. Nauchn. Sem. POMI, 269, POMI, St. Petersburg, 2000, 322–338; J. Math. Sci. (N. Y.), 115:1 (2003), 2066–2075
Citation in format AMSBIB
\Bibitem{SolFas00}
\by V.~A.~Solonnikov, A.~Fasano
\paper One-dimensional parabolic problem arising in the study of some free boundary problems
\inbook Questions of quantum field theory and statistical physics. Part~16
\serial Zap. Nauchn. Sem. POMI
\yr 2000
\vol 269
\pages 322--338
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl1322}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1805868}
\zmath{https://zbmath.org/?q=an:1031.35153}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2003
\vol 115
\issue 1
\pages 2066--2075
\crossref{https://doi.org/10.1023/A:1022616300191}
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  • https://www.mathnet.ru/eng/znsl/v269/p322
    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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