Is it possible to say that $\|u\|_{H_{0}^{2}(\Omega)}$ is equivalent to $\|\Delta u\|_{2}$?
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The questions you asked so far were titled "An equivalent norm", "An inequality-Is it possible?", "An integral inequality", and "An imbedding question". Consider using more descriptive titles in the future. The column on the right titled Related has a few good examples of such titles. – 40 votes Jul 17 '13 at 22:32