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. 
On the best constant of Hardy―Sobolev inequalities
Abstract We obtain the sharp constant for the Hardy-Sobolev inequality involving the distance to the origin. This inequality is equivalent to a limiting Caffarelli–Kohn–Nirenberg inequality. In threeExpand
Existence of extremal functions for a Hardy–Sobolev inequality
Abstract We present the best constant and the extremal functions for an Improved Hardy–Sobolev inequality. We prove that, under a proper transformation, this inequality is equivalent to the SobolevExpand
The optimal Euclidean Lp-Sobolev logarithmic inequality
We prove an optimal logarithmic Sobolev inequality in W1,p(Rd). Explicit minimizers are given. This result is connected with best constants of a special class of Gagliardo–Nirenberg-type inequalities.
Hardy-Sobolev Inequalities in a Cone
The attainability of the exact constant in the Hardy-Sobolev inequality is established in an arbitrary cone in ℝn. Bibliography: 17 titles.
Remarks on inequalities of Hardy-Sobolev Type
We obtain the sharp constants of some Hardy-Sobolev-type inequalities proved by Balinsky et al. (Banach J Math Anal 2(2):94-106).2000 Mathematics Subject Classification: Primary 26D10; 46E35.
Best constant in Sobolev trace inequalities on the half-space
Using a mass transportation method, we study optimal Sobolev trace inequalities on the half-space and prove a conjecture made by Escobar in 1988 about the minimizers.
The sharp Sobolev inequality in quantitative form
A quantitative version of the sharp Sobolev inequality in W (R), 1 < p < n, is established with a remainder term involving the distance from extremals.
SHARP MORREY-SOBOLEV INEQUALITIES AND THE DISTANCE FROM EXTREMALS
Quantitative versions of sharp estimates for the supremum of Sobolev functions in W 1,p (R n ), p > n, with remainder terms depending on the distance from the families of extremals, are established.
Best constants for Sobolev inequalities for higher order fractional derivatives
We obtain sharp constants for Sobolev inequalities for higher order fractional derivatives. As an application, we give a new proof of a theorem of W. Beckner concerning conformally invariantExpand
Some remarks on Sobolev type inequalities
We extend two Sobolev type inequalities for balls to arbitrary smooth bounded domains. In the case of balls, one inequality is due to Brezis and Lieb and another is due to Escobar. The extension hasExpand
...
1
2
3
4
5
...

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
  • Sere. Mat. Univ. Padova,
  • 1967
Disuguaglianze di Sobolev sulle ipersuper]ici minimali, l~end
  • Sere. Mat. Univ. Padova
  • 1967
Sut minimo dell'iutegrale del gradiente eli una ]unzione
  • Ann. Scuola Norm. Sup. Pisa, 19
  • 1965
Sut minimo dell'iutegrale del gradiente eli una ]unzione, Ann. Scuola Norm
  • Sup. Pisa
  • 1965
Distribuzio~i a venti derivate misure
  • Ann. Scuola Norm. Sup. Pisa
  • 1964
...
1
2
3
...