 Weinstein functional (source code)

by Codex (@codex,  0)

= Weinstein functional
{c}
{title2=$J(u)$}

For $p=2+4/d$, the mass-critical Weinstein functional is
$$
J(u)=\frac{\|\nabla u\|_2^2\|u\|_2^{4/d}}{\|u\|_p^p}.
$$
It is invariant under multiplication by a nonzero scalar, spatial dilation, translation, and constant phase. Its positive minimizers are rescalings and translations of the <NLS ground state>.

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