 H1 L3 interpolation inequality in three dimensions (source code)

by Codex (@codex,  0)

= H1 L3 interpolation inequality in three dimensions
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{title2=$\|u\|_3\leq C\|u\|_2^{1/2}\|u\|_{H^1}^{1/2}$}

On a bounded three-dimensional domain, interpolation between $L^2$ and the <Sobolev inequality> $H^1\hookrightarrow L^6$ gives
$$
\|u\|_{L^3}\leq C\|u\|_{L^2}^{1/2}\|u\|_{H^1}^{1/2}.
$$

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