Gagliardo-Nirenberg interpolation inequality (source code)

= Gagliardo-Nirenberg interpolation inequality
{c}
{wiki}

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
{c}
{synonym}