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Zapiski Nauchnykh Seminarov POMI, 2010, Volume 374, Pages 121–135 (Mi znsl3598)  
This article is cited in 2 scientific papers (total in 2 papers)

On equation of minimal surface in $\mathbb R^3$: different representations, properties of exact solutions, conservation laws

E. Sh. Gutshabash

St. Petersburg State University, Faculty of Physics, St. Petersburg, Russia
Full-text PDF (229 kB) Citations (2)
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Abstract: Various representations of the equation of minimal surface in $\mathbb R^3$ are considered. Properties of exact solutions are studied and a procedure to construct the corresponding conservation laws is suggested. Links between the solutions of this equation and those of the elliptic version of the Monge–Ampere equation are found. Bibl. – 19 titles.
Key words and phrases: equation of minimal surface in $\mathbb R^3$, exact solutions, Cauchy–Green formula, conservation laws, Monge–Ampere equation.
Received: 12.04.2010
English version:
Journal of Mathematical Sciences (New York), 2010, Volume 168, Issue 6, Pages 829–836
DOI: https://doi.org/10.1007/s10958-010-0031-x
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: E. Sh. Gutshabash, “On equation of minimal surface in $\mathbb R^3$: different representations, properties of exact solutions, conservation laws”, Questions of quantum field theory and statistical physics. Part 21, Zap. Nauchn. Sem. POMI, 374, POMI, St. Petersburg, 2010, 121–135; J. Math. Sci. (N. Y.), 168:6 (2010), 829–836
Citation in format AMSBIB
\Bibitem{Gut10}
\by E.~Sh.~Gutshabash
\paper On equation of minimal surface in~$\mathbb R^3$: different representations, properties of exact solutions, conservation laws
\inbook Questions of quantum field theory and statistical physics. Part~21
\serial Zap. Nauchn. Sem. POMI
\yr 2010
\vol 374
\pages 121--135
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl3598}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2010
\vol 168
\issue 6
\pages 829--836
\crossref{https://doi.org/10.1007/s10958-010-0031-x}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-77955281078}
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  • https://www.mathnet.ru/eng/znsl/v374/p121
    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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