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

This article is cited in 4 scientific papers (total in 4 papers)

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:

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
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    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  mathscinet  isi  elib  elib
    2. A. K. Gushchin, “The boundary values of solutions of an elliptic equation”, Sb. Math., 210:12 (2019), 1724–1752  mathnet  crossref  crossref  mathscinet  isi  elib
    3. 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  mathnet  crossref  crossref  mathscinet  isi  elib
    4. A. K. Guschin, “Obobscheniya prostranstva nepreryvnykh funktsii; teoremy vlozheniya”, Matem. sb., 211:11 (2020), 54–71  mathnet  crossref
  • Математический сборник Sbornik: Mathematics (from 1967)
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