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Mat. Sb., 2018, Volume 209, Number 6, Pages 47–64 (Mi msb8980)  

This article is cited in 1 scientific paper (total in 1 paper)

The Luzin area integral and the nontangential maximal function for solutions to a second-order elliptic equation

A. K. Gushchin

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: The paper is concerned with the relationship between the nontangential maximal function of the solution to a Dirichlet problem with an $L_p$-boundary function, $p>1$, for a second-order elliptic equation and the Luzin area integral. The equation is considered in the self-adjoint form without lower-degree terms. The $L_p$-norm of the nontangential maximal function of the solution $u$ is estimated from above and below in terms of the squared $L_2(\partial Q)$-norm of the area integral of $v=|u|^{p/2}$. Here the coefficients of the equation need not be smooth in the domain.
Bibliography: 33 titles.

Keywords: elliptic equation, Dirichlet problem, nontangential maximal function, Luzin area integral.

Funding Agency Grant Number
Russian Science Foundation 14-50-00005
This work was supported by the Russian Science Foundation under grant 14-50-00005.


DOI: https://doi.org/10.4213/sm8980

Full text: PDF file (680 kB)
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English version:
Sbornik: Mathematics, 2018, 209:6, 823–839

Bibliographic databases:

Document Type: Article
UDC: 517.956.223
MSC: Primary 35J25; Secondary 35J67
Received: 14.06.2017

Citation: A. K. Gushchin, “The Luzin area integral and the nontangential maximal function for solutions to a second-order elliptic equation”, Mat. Sb., 209:6 (2018), 47–64; Sb. Math., 209:6 (2018), 823–839

Citation in format AMSBIB
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  • https://doi.org/10.4213/sm8980
  • http://mi.mathnet.ru/eng/msb/v209/i6/p47

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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. 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  mathnet  crossref  crossref  isi  elib  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
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