On the estimation of $\int|\nabla u|^2dx$ for solutions of second order elliptic equations

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.