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.
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, Trudy Mat. Inst. Steklova, 289, MAIK Nauka/Interperiodica, Moscow, 2015, 145–162; Proc. Steklov Inst. Math., 289 (2015), 134–151
\Bibitem{Gus15}
\by A.~K.~Gushchin
\paper V.A.~Steklov's work on equations of mathematical physics and development of his results in this field
\inbook Selected issues of mathematics and mechanics
\bookinfo Collected papers. In commemoration of the 150th anniversary of Academician Vladimir Andreevich Steklov
\serial Trudy Mat. Inst. Steklova
\yr 2015
\vol 289
\pages 145--162
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm3613}
\crossref{https://doi.org/10.1134/S0371968515020089}
\elib{https://elibrary.ru/item.asp?id=23738466}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2015
\vol 289
\pages 134--151
\crossref{https://doi.org/10.1134/S0081543815040082}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000358577300008}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84938821617}
Linking options:
https://www.mathnet.ru/eng/tm3613
https://doi.org/10.1134/S0371968515020089
https://www.mathnet.ru/eng/tm/v289/p145
This publication is cited in the following 8 articles:
A. K. Gushchin, “On Dirichlet problem”, Theoret. and Math. Phys., 218:1 (2024), 51–67
A. K. Gushchin, “On some properties of elliptic partial differential equation solutions”, Int. J. Mod. Phys. A, 37:20 (2022), 2243002–9
A. K. Gushchin, “The boundary values of solutions of an elliptic equation”, Sb. Math., 210:12 (2019), 1724–1752
A. K. Gushchin, “On the Existence of $L_2$ Boundary Values of Solutions to an Elliptic Equation”, Proc. Steklov Inst. Math., 306 (2019), 47–65
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
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
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
V. V. Kozlov, V. P. Pavlov, A. G. Sergeev, “Vladimir Andreevich Steklov (1863–1926)”, Proc. Steklov Inst. Math., 289 (2015), 1–9
Citation in format AMSBIB
Contact us: