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 Tr. Mat. Inst. Steklova, 2015, Volume 289, Pages 145–162 (Mi tm3613)

V.A. Steklov's work on equations of mathematical physics and development of his results in this field

A. K. Gushchin

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia

Abstract: This paper is an extended account of the author's talk at the International Conference “Contemporary Problems of Mathematics, Mechanics, and Mathematical Physics” dedicated to the 150th anniversary of Vladimir Andreevich Steklov. Steklov's main studies on the solvability of boundary value problems for equations of mathematical physics are briefly described, and the further development of this field of research is surveyed. The main attention is focused on the statements of the Dirichlet problem and the conditions on the domain and given functions under which solvability theorems are valid.

 Funding Agency Grant Number Russian Foundation for Basic Research 13-01-00065-à

DOI: https://doi.org/10.1134/S0371968515020089

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English version:
Proceedings of the Steklov Institute of Mathematics, 2015, 289, 134–151

Bibliographic databases:

UDC: 517.956.223

Citation: A. K. Gushchin, “V.A. Steklov's work on equations of mathematical physics and development of his results in this field”, Selected issues of mathematics and mechanics, Collected papers. In commemoration of the 150th anniversary of Academician Vladimir Andreevich Steklov, Tr. Mat. Inst. Steklova, 289, MAIK Nauka/Interperiodica, Moscow, 2015, 145–162; Proc. Steklov Inst. Math., 289 (2015), 134–151

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/tm3613
• https://doi.org/10.1134/S0371968515020089
• http://mi.mathnet.ru/eng/tm/v289/p145

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. V. V. Kozlov, V. P. Pavlov, A. G. Sergeev, “Vladimir Andreevich Steklov (1863–1926)”, Proc. Steklov Inst. Math., 289 (2015), 1–9
2. A. K. Gushchin, “$L_p$-estimates for the nontangential maximal function of the solution to a second-order elliptic equation”, Sb. Math., 207:10 (2016), 1384–1409
3. A. K. Gushchin, “The Luzin area integral and the nontangential maximal function for solutions to a second-order elliptic equation”, Sb. Math., 209:6 (2018), 823–839
4. A. K. Gushchin, “A criterion for the existence of $L_p$ boundary values of solutions to an elliptic equation”, Proc. Steklov Inst. Math., 301 (2018), 44–64
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