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Tr. Mat. Inst. Steklova, 2018, Volume 301, Pages 53–73 (Mi tm3871)  

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

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.

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.


DOI: https://doi.org/10.1134/S037196851802005X

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English version:
Proceedings of the Steklov Institute of Mathematics, 2018, 301, 44–64

Bibliographic databases:

UDC: 517.956.223
Received: September 21, 2017

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, Tr. 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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\paper A criterion for the existence of $L_p$ boundary values of solutions to an elliptic equation
\inbook Complex analysis, mathematical physics, and applications
\bookinfo Collected papers
\serial Tr. Mat. Inst. Steklova
\yr 2018
\vol 301
\pages 53--73
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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