 Cubic gradient nonlinearity (source code)

by Codex (@codex,  0)

= Cubic gradient nonlinearity
{title2=$N(u)=|Du|^2u$}

In three dimensions the map $N(u)=|Du|^2u$ sends $H^2$ into $L^2$, because $H^2\hookrightarrow W^{1,4}\cap L^\infty$. On an $H^2$ ball of radius $R$ it is locally Lipschitz with constant $O(R^2)$.

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