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I have a equation something like this:

$\int_U |\Delta u|^2dx \le C\int_U |D^2 u|^2dx$ . where $u \in C_c^{\infty}$ implies that u belongs to a compactly supported smooth function .

I would like to know how i can integrate it using integration by parts. Thank you for your kind help. Its true that when $C=1$ its an equality.

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    It turns out that the $\nabla$ operator came from an edit from another user, who has now reinstated the original $D$. That raises the question what $D$ denotes. More generally, @Theorem, in the future please take more care to introduce any notation that you use that can't be assumed to obvious to everyone.2012-06-13

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