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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2018, Volume 301, Pages 53–73
DOI: https://doi.org/10.1134/S037196851802005X
(Mi tm3871)
 

This article is cited in 3 scientific papers (total in 3 papers)

A criterion for the existence of $L_p$ boundary values of solutions to an elliptic equation

A. K. Gushchin

Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia
Full-text PDF (290 kB) Citations (3)
References:
Abstract: The paper is devoted to the study of the boundary behavior of solutions to a second-order elliptic equation. A criterion is established for the existence in $L_p$, $p>1$, of a boundary value of a solution to a homogeneous equation in the self-adjoint form without lower order terms. Under the conditions of this criterion, the solution belongs to the space of $(n-1)$-dimensionally continuous functions; thus, the boundary value is taken in a much stronger sense. Moreover, for such a solution to the Dirichlet problem, estimates for the nontangential maximal function and for an analog of the Lusin area integral hold.
Keywords: elliptic equation, boundary value, Dirichlet problem, Lusin area integral.
Funding agency Grant number
Russian Academy of Sciences - Federal Agency for Scientific Organizations PRAS-18-01
This work is supported by the Program of the Presidium of the Russian Academy of Sciences no. 01 “Fundamental Mathematics and Its Applications” under grant PRAS-18-01.
Received: September 21, 2017
English version:
Proceedings of the Steklov Institute of Mathematics, 2018, Volume 301, Pages 44–64
DOI: https://doi.org/10.1134/S0081543818040053
Bibliographic databases:
Document Type: Article
UDC: 517.956.223
Language: Russian
Citation: A. K. Gushchin, “A criterion for the existence of $L_p$ boundary values of solutions to an elliptic equation”, Complex analysis, mathematical physics, and applications, Collected papers, Trudy Mat. Inst. Steklova, 301, MAIK Nauka/Interperiodica, Moscow, 2018, 53–73; Proc. Steklov Inst. Math., 301 (2018), 44–64
Citation in format AMSBIB
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  • This publication is cited in the following 3 articles:
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    Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
     
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