The estimates of the solution of the Dirichlet problem with boundary function from $L_p$ for a~second-order elliptic equation
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 1 (2011), pp. 53-67.

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We study the solvability of the Dirichlet problem for a second-order elliptic equation with measurable and bounded coefficients. Assuming that coefficients of equation are Dini-continued on the boundary, it is established that there is the unique solution of the Dirichlet problem with boundary function from $L_p$, $p>1$. We prove the estimate of the analogue of area integral.
Mots-clés : elliptic equation
Keywords: Dirichlet problem, functional space.
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A. K. Gushchin. The estimates of the solution of the Dirichlet problem with boundary function from $L_p$ for a~second-order elliptic equation. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 1 (2011), pp. 53-67. http://geodesic.mathdoc.fr/item/VSGTU_2011_1_a7/

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