Gagliardo-Nirenberg interpolation inequality
= Gagliardo-Nirenberg interpolation inequality
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The Gagliardo-Nirenberg interpolation inequalities bound an intermediate derivative norm by powers of a higher derivative norm and a lower norm. In two dimensions, one useful case is
$$
\|\nabla f\|_4^2\leq C\|\nabla f\|_2\|D^2f\|_2.
$$
= Gagliardo-Nirenberg inequality
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