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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]:
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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2013, Issue 1(30), Pages 53–69 (Mi vsgtu1162)  

This article is cited in 2 scientific papers (total in 2 papers)

Procedings of the 3nd International Conference "Mathematical Physics and its Applications"
Equations of Mathematical Physics

$L_p$-estimates of the nontangential maximal function for solutions a second-order elliptic equation solutions

A. K. Gushchin

Steklov Mathematical Institute of the Russian Academy of Sciences, Moscow, 119991, Russia

Abstract: The work contains the survey of results related to the study of near the boundary behavior of the solution of the Dirichlet problem with the boundary function in $L_p,$ $p > 1$ for a second-order elliptic equation. There are new statements and some unsolved problems in this direction.

Keywords: elliptic equation, Dirichlet problem, function space

Funding Agency Grant Number
Russian Foundation for Basic Research 10-01-00178
Ministry of Education and Science of the Russian Federation 2928.2012.1


DOI: https://doi.org/10.14498/vsgtu1162

Full text: PDF file (254 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
References: PDF file   HTML file

Bibliographic databases:

UDC: 517.956.223
MSC: Primary 35D05; Secondary 35J25, 35B30, 35R05, 35B4
Original article submitted 13/XI/2012
revision submitted – 19/I/2013

Citation: A. K. Gushchin, “$L_p$-estimates of the nontangential maximal function for solutions a second-order elliptic equation solutions”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 1(30) (2013), 53–69

Citation in format AMSBIB
\Bibitem{Gus13}
\by A.~K.~Gushchin
\paper $L_p$-estimates of the nontangential maximal function for solutions a second-order elliptic equation solutions
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2013
\vol 1(30)
\pages 53--69
\mathnet{http://mi.mathnet.ru/vsgtu1162}
\crossref{https://doi.org/10.14498/vsgtu1162}


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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. P. Mikhailov, “O suschestvovanii granichnykh znachenii u reshenii ellipticheskikh uravnenii”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 1(30) (2013), 97–105  mathnet  crossref
    2. A. K. Gushchin, “The boundary values of solutions of an elliptic equation”, Sb. Math., 210:12 (2019), 1724–1752  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
  • Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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