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Mathematics of the USSR-Izvestiya, 1979, Volume 13, Issue 2, Pages 335–347
DOI: https://doi.org/10.1070/IM1979v013n02ABEH002046 (Mi im1926) 		 
This article is cited in 12 scientific papers (total in 12 papers)

On the maximum principle for nonlinear parabolic and elliptic equations

N. V. Krylov
English version PDF (575 kB) Citations (12)
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DOI: https://doi.org/10.1070/IM1979v013n02ABEH002046
Abstract: A maximum principle in Sobolev spaces is proved for nonlinear elliptic and parabolic equations. The proof is based on estimates for the maximum of the solutions of a parabolic equation with measurable coefficients, in terms of the $\mathscr L_p$ norm of the right side. The results of the paper are analogous to results of A. D. Aleksandrov on elliptic equations.
Bibliography: 10 titles.
Received: 11.05.1977
Russian version:
Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya, 1978, Volume 42, Issue 5, Pages 1050–1062
Bibliographic databases:
UDC: 517.9
MSC: Primary 35K55; Secondary 35B45, 35J60
Language: English
Original paper language: Russian
Citation: N. V. Krylov, “On the maximum principle for nonlinear parabolic and elliptic equations”, Izv. Akad. Nauk SSSR Ser. Mat., 42:5 (1978), 1050–1062; Math. USSR-Izv., 13:2 (1979), 335–347
Citation in format AMSBIB
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\paper On the maximum principle for nonlinear parabolic and elliptic equations
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\yr 1978
\vol 42
\issue 5
\pages 1050--1062
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\transl
\jour Math. USSR-Izv.
\yr 1979
\vol 13
\issue 2
\pages 335--347
\crossref{https://doi.org/10.1070/IM1979v013n02ABEH002046}
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  • https://doi.org/10.1070/IM1979v013n02ABEH002046
  • https://www.mathnet.ru/eng/im/v42/i5/p1050
    • This publication is cited in the following 12 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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    Abstract page:646
    Russian version PDF:302
    English version PDF:17
    References:55
    First page:1
     
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