Geodesic
On the estimation of $\int|\nabla u|^2dx$ for solutions of second order elliptic equations
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 2 (2008), pp. 145-147.

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In this article an inequality is proved, which estimates the norm in $L_2$ of the gradient of a generalized (belonging to $W^1_{2,loc}$) solution of a second order elliptic equation over the strict interior subregion through the norms in $L_2$ of the solution itself and the right hand side of the equation. 
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V. Zh. Dumanyan. On the estimation of $\int|\nabla u|^2dx$ for solutions of second order elliptic equations. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 2 (2008), pp. 145-147. http://geodesic.mathdoc.fr/item/UZERU_2008_2_a12/

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[2] V. P. Mikhailov, Differentsialnye uravneniya v chastnykh proizvodnykh, Nauka, M., 1987

[3] V. S. Vladimirov, Uravneniya matematicheskoi fiziki, Nauka, M., 1981 | MR