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Zapiski Nauchnykh Seminarov POMI, 1997, Volume 249, Pages 20–39 (Mi znsl578)  

This article is cited in 8 scientific papers (total in 8 papers)

On the partial regularity up to the boundary of weak solutions to quasilinear parabolic systems with quadratic growth

A. A. Arkhipova

Saint-Petersburg State University
Full-text PDF (261 kB) Citations (8)
Abstract: We consider quasilinear nondiagonal parabolic systems with quadratic growth on the gradient in a parabolic cylinder $Q$. Under Dirichlet and Neumann boundary conditions partial Hölder continuity up to the lateral surface of $Q$ of solutions $u\in W_2^{1,1} (Q)\cap L^\infty(Q)$ is proved. Hausdorff dimension of a singular set is estimated. In the proof we get of the maximum principle theorem for corresponding model linear problems.
Received: 05.05.1997
English version:
Journal of Mathematical Sciences (New York), 2000, Volume 101, Issue 5, Pages 3385–3397
DOI: https://doi.org/10.1007/BF02680140
Bibliographic databases:
UDC: 517.9
Language: English
Citation: A. A. Arkhipova, “On the partial regularity up to the boundary of weak solutions to quasilinear parabolic systems with quadratic growth”, Boundary-value problems of mathematical physics and related problems of function theory. Part 29, Zap. Nauchn. Sem. POMI, 249, POMI, St. Petersburg, 1997, 20–39; J. Math. Sci. (New York), 101:5 (2000), 3385–3397
Citation in format AMSBIB
\Bibitem{Ark97}
\by A.~A.~Arkhipova
\paper On~the partial regularity up to the boundary of weak solutions to quasilinear parabolic systems with quadratic growth
\inbook Boundary-value problems of mathematical physics and related problems of function theory. Part~29
\serial Zap. Nauchn. Sem. POMI
\yr 1997
\vol 249
\pages 20--39
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl578}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1698511}
\zmath{https://zbmath.org/?q=an:0969.35032}
\transl
\jour J. Math. Sci. (New York)
\yr 2000
\vol 101
\issue 5
\pages 3385--3397
\crossref{https://doi.org/10.1007/BF02680140}
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  • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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