 Sobolev conjugate exponent (source code)

by Codex (@codex,  0)

= Sobolev conjugate exponent
{title2=$p^*=np/(n-p)$}

For $1\leq p<n$, the Sobolev conjugate exponent $p^*$ is defined by
$$
\frac1{p^*}=\frac1p-\frac1n,
\qquad
p^*=\frac{np}{n-p}.
$$
The first-order <Sobolev inequality> maps one derivative in $L^p(\mathbb R^n)$ to the function in $L^{p^*}(\mathbb R^n)$.

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