Geodesic
$L_p$-estimates for the nontangential maximal function of the solution to a~second-order elliptic equation
Sbornik. Mathematics, Tome 207 (2016) no. 10, pp. 1384-1409

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The paper is concerned with the properties of the solution to a Dirichlet problem for a homogeneous second-order elliptic equation with $L_p$-boundary function, $p>1$. The same conditions are imposed on the coefficients of the equation and the boundary of the bounded domain as were used to establish the solvability of this problem. The $L_p$-norm of the nontangential maximal function is estimated in terms of the $L_p$-norm of the boundary value. This result depends on a new estimate, proved below, for the nontangential maximal function in terms of an analogue of the Lusin area integral. Bibliography: 31 titles.
Keywords: Dirichlet problem, nontangential maximal function.
Mots-clés : elliptic equation 
@article{SM_2016_207_10_a2,
     author = {A. K. Gushchin},
     title = {$L_p$-estimates for the nontangential maximal function of the solution to a~second-order elliptic equation},
     journal = {Sbornik. Mathematics},
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     volume = {207},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2016_207_10_a2/}
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A. K. Gushchin. $L_p$-estimates for the nontangential maximal function of the solution to a~second-order elliptic equation. Sbornik. Mathematics, Tome 207 (2016) no. 10, pp. 1384-1409. http://geodesic.mathdoc.fr/item/SM_2016_207_10_a2/