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## Poincare’s Inequality

Suppose $D \subset \Bbb{R}^N$ is bounded with respect to one direction. Prove that there exists $C$ which is independent of $D$ such that $\displaystyle \forall u \in H_0^1(D),\ \int_D u^2 \leq C^2 \int_D | \nabla u|^2$.