# Best constant in Sobolev inequality

@article{Talenti1976BestCI,
title={Best constant in Sobolev inequality},
author={G. Talenti},
journal={Annali di Matematica Pura ed Applicata},
year={1976},
volume={110},
pages={353-372}
}
• G. Talenti
• Published 1976
• Mathematics
• Annali di Matematica Pura ed Applicata
SummaryThe best constant for the simplest Sobolev inequality is exhibited. The proof is accomplished by symmetrizations (rearrangements in the sense of Hardy-Littlewood) and one-dimensional calculus of variations.
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#### References

SHOWING 1-10 OF 21 REFERENCES
Minimum Value for c in the Sobolev Inequality $\| {\phi ^3 } \|\leqq c\| {\nabla \phi } \|^3$
It is shown that the minimum value for c is $4/3 \sqrt 3 \pi ^2 \cong .0780$ for $\phi$ of function class $C^0$ piecewise $C^2$ in real Euclidean 3-space.
Distribuzioni aventi derivate misure insiemi di perimetro localmente finito
L’accès aux archives de la revue « Annali della Scuola Normale Superiore di Pisa, Classe di Scienze » (http://www.sns.it/it/edizioni/riviste/annaliscienze/) implique l’accord avec les conditionsExpand
Minimum value ]or c in the Sobotev inequality
• SIAM J. Appl. Math
• 1971
Disuguaglianze di Sobolev sulle ipersuper]ici minimali, l~end