Best constant in Sobolev inequality

@article{Talenti1976BestCI,
  title={Best constant in Sobolev inequality},
  author={Giorgio Talenti},
  journal={Annali di Matematica Pura ed Applicata},
  year={1976},
  volume={110},
  pages={353-372}
}
  • G. Talenti
  • Published 1 December 1976
  • Mathematics, Materials Science
  • 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

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.

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.

On Sobolev type integral inequalities

  • B. G. Pachpatte
  • Mathematics
    Proceedings of the Royal Society of Edinburgh: Section A Mathematics
  • 1986
Synopsis The aim of this paper is to establish some new integral inequalities of the Sobolev type involving functions of several independent variables. The analysis used in the proofs is elementary

On Sharp Sobolev Embedding and The Logarithmic Sobolev Inequality

The purpose of this note is to give a short proof of the Gross logarithmic Sobolev inequality using the asymptotics of the sharp L2 Sobolev constant and the product structure of Euclidean space. Let
...

References

SHOWING 1-10 OF 13 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.

Diseguaglianze di Sobolev sulle ipersuperfici minimali

L’accès aux archives de la revue « Rendiconti del Seminario Matematico della Università di Padova » (http://rendiconti.math.unipd.it/) implique l’accord avec les conditions générales d’utilisation

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 conditions

Applications of Functional Analysis in Mathematical Physics

  • J. McLeod
  • Mathematics
    The Mathematical Gazette
  • 1964

Distribuzio~i a venti derivate misure

  • Ann. Scuola Norm. Sup. Pisa, 18
  • 1964

On a theorem o] ]unetionat analysis (in russian)

  • Mat. Sb., 4
  • 1938