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Zapiski Nauchnykh Seminarov POMI, 2013, Volume 411, Pages 103–118 (Mi znsl5634)  
This article is cited in 4 scientific papers (total in 4 papers)

Sobolev regularity for the Monge–Ampère equation, with application to the semigeostrophic equations

Alessio Figalli

The University of Texas at Austin, Mathematics Dept. RLM 8.100, 2515 Speedway Stop C1200, Austin, Texas 78712-1202 USA
Full-text PDF (260 kB) Citations (4)
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Abstract: In this note we review some recent results on the Sobolev regularity of solutions to the Monge–Ampère equation, and show how these estimates can be used to prove some global existence results for the semigeostrophic equations.
Key words and phrases: Monge–Ampère equation, Sobolev regularity, semigeostrophic equations.
Received: 25.02.2013
English version:
Journal of Mathematical Sciences (New York), 2014, Volume 196, Issue 2, Pages 175–183
DOI: https://doi.org/10.1007/s10958-013-1649-2
Bibliographic databases:
Document Type: Article
UDC: 517.972+517.958:531.32
Language: English
Citation: Alessio Figalli, “Sobolev regularity for the Monge–Ampère equation, with application to the semigeostrophic equations”, Representation theory, dynamical systems, combinatorial methods. Part XXII, Zap. Nauchn. Sem. POMI, 411, POMI, St. Petersburg, 2013, 103–118; J. Math. Sci. (N. Y.), 196:2 (2014), 175–183
Citation in format AMSBIB
\Bibitem{Fig13}
\by Alessio~Figalli
\paper Sobolev regularity for the Monge--Amp\`ere equation, with application to the semigeostrophic equations
\inbook Representation theory, dynamical systems, combinatorial methods. Part~XXII
\serial Zap. Nauchn. Sem. POMI
\yr 2013
\vol 411
\pages 103--118
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5634}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3048271}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2014
\vol 196
\issue 2
\pages 175--183
\crossref{https://doi.org/10.1007/s10958-013-1649-2}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84897100531}
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  • https://www.mathnet.ru/eng/znsl/v411/p103
    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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