This article is cited in 2 papers

Communications
Mathematics

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

V. Zh. Dumanyan

Chair of Numerical Analysis and Mathematical Modelling YSU, Armenia

Abstract: 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.

UDC: 517.9

Received: 19.11.2007