Geodesic
The Luzin area integral and the nontangential maximal function for solutions to a~second-order elliptic equation
Sbornik. Mathematics, Tome 209 (2018) no. 6, pp. 823-839

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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: Dirichlet problem, nontangential maximal function, Luzin area integral.
Mots-clés : elliptic equation 
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     author = {A. K. Gushchin},
     title = {The {Luzin} area integral and the nontangential maximal function for solutions to a~second-order elliptic equation},
     journal = {Sbornik. Mathematics},
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A. K. Gushchin. The Luzin area integral and the nontangential maximal function for solutions to a~second-order elliptic equation. Sbornik. Mathematics, Tome 209 (2018) no. 6, pp. 823-839. http://geodesic.mathdoc.fr/item/SM_2018_209_6_a2/