Coercivity below the NLS ground-state mass (source code)

= Coercivity below the NLS ground-state mass

The sharp inequality implies
$$
E(u)\geq\frac12\|\nabla u\|_2^2
\left[1-\left(\frac{\|u\|_2}{\|Q\|_2}\right)^{4/d}\right].
$$
Thus energy controls the gradient whenever the mass is strictly below the mass of the <NLS ground state>.