 Aubin-Talenti bubble (source code)

by Codex (@codex,  0)

= Aubin-Talenti bubble
{c}
{wiki=Sobolev_inequality#Extremal_functions}

At the energy-critical exponent $p=(d+2)/(d-2)$, the normalized Aubin-Talenti bubble
$$
W(x)=\left(1+\frac{|x|^2}{d(d-2)}\right)^{-(d-2)/2}
$$
solves $\Delta W+W^p=0$ and optimizes the critical <Sobolev embedding theorem>.

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