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.