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Ufa Mathematical Journal, 2016, Volume 8, Issue 1, Pages 68–78
DOI: https://doi.org/10.13108/2016-8-1-68 (Mi ufa316) 		 
This article is cited in 3 scientific papers (total in 3 papers)

On convergence of polynomial solutions of minimal surface

A. A. Klyachin, I. V. Truhlyaeva

Volgograd State University, Universitetsky av., 100, 400062, Volgograd, Russia
English full-text Citations (3)
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DOI: https://doi.org/10.13108/2016-8-1-68
Abstract: In this paper we consider the polynomial approximate solutions of the Dirichlet problem for minimal surface equation. It is shown that under certain conditions on the geometric structure of the domain the absolute values of the gradients of the solutions are bounded as the degree of these polynomials increases. The obtained properties imply the uniform convergence of approximate solutions to the exact solution of the minimal surface equation.
Keywords: minimal surface equation, uniform convergence, approximate solution.
Funding agency Grant number
Russian Foundation for Basic Research 15-41-02517-р_поволжье_а
The work is supported by RFBR (project no. 15-41-02517-r_povolzhe_a).
Received: 15.05.2015
Russian version:
Ufimskii Matematicheskii Zhurnal, 2016, Volume 8, Issue 1, Pages 72–83
Bibliographic databases:
Document Type: Article
UDC: 517.9
MSC: 35J25, 35J93, 65N30
Language: English
Original paper language: Russian
Citation: A. A. Klyachin, I. V. Truhlyaeva, “On convergence of polynomial solutions of minimal surface”, Ufimsk. Mat. Zh., 8:1 (2016), 72–83; Ufa Math. J., 8:1 (2016), 68–78
Citation in format AMSBIB
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  • https://doi.org/10.13108/2016-8-1-68
  • https://www.mathnet.ru/eng/ufa/v8/i1/p72
    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Уфимский математический журнал
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