Geodesic
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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     author = {A. K. Gushchin},
     title = {The estimates of the solution of the {Dirichlet} problem with boundary function from $L_p$ for a~second-order elliptic equation},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {53--67},
     publisher = {mathdoc},
     number = {1},
     year = {2011},
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     url = {http://geodesic.mathdoc.fr/item/VSGTU_2011_1_a7/}
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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/