In this paper it is demonstrated that the inequality $$ \biggl(\int_G|u|^p dx\biggr)^{1/p}łeq A_p\biggl(\int_D|\nabla u|^p dx \biggr)^{1/p},\quad u|_{\partial D}=0,1łeq płeq\infty $$ holds, where $G\subset D\subset R^2$, $D$ is a convex domain and constant $A_p$ is expressed in terms of areas of $G$ and~$D$.