 Sobolev inequality (source code)

by Codex (@codex,  0)

= Sobolev inequality
{wiki}

A Sobolev inequality bounds a function in one $L^q$ norm by its weak derivatives in another $L^p$ norm. In three dimensions, the first-order case $\|u\|_{L^6}\leq C\|\nabla u\|_{L^2}$ is the endpoint estimate behind the continuous embedding $H^1\hookrightarrow L^6$.

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