Best constant in Sobolev inequality

Giorgio Talenti

doi:10.1007/bf02418013

journal article Dec 01, 1976

Best constant in Sobolev inequality

Giorgio Talenti

Annali di Matematica Pura ed Applicata Vol. 110 No. 1 pp. 353-372 · Springer Science and Business Media LLC

View at Publisher Save 10.1007/bf02418013

Topics

No keywords indexed for this article. Browse by subject →

References

13

[1]

L. Bers - F. John - M. Schechter,Partial Differential Equations, Interscience (1964)

[2]

G. A. Bliss,An integral inequality, Journal London Math. Soc.,5 (1930). 10.1112/jlms/s1-5.1.40

[3]

H. Federer,Curvature measure, Trans. Amer. Math. Soc.,93 (1959). 10.1090/s0002-9947-1959-0110078-1

[4]

H. Federer - W. Fleming,Normal and integral currents, Annals of Math.,72 (1960). 10.2307/1970227

[5]

W. Fleming,Functions whose partial derivatives are measures, Illinois J. Math.,4 (1960). 10.1215/ijm/1255456061

[6]

W. Fleming - R. Rishel,An integral formula for total gradient variation, Arch. Math.,11 (1960). 10.1007/bf01236935

[7]

M. Miranda,Distribuzioni aventi derivate misure, Ann. Scuola Norm. Sup. Pisa,18 (1964).

[8]

M. Miranda,Sul minimo dell'integrale del gradiente di una funzione, Ann. Scuola Norm. Sup. Pisa,19 (1965).

[9]

M. Miranda,Disuguaglianze di Sobolev sulle ipersuperfici minimali, Rend. Sem. Mat. Univ. Padova,38 (1967).

[10]

G. Rosen,Minimum value for c in the Sobolev inequality, SIAM J. Appl. Math.,21 (1971). 10.1137/0121004

[11]

S. L. Sobolev,On a theorem of functional analysis (in russian), Mat. Sb.,4 (1938).

[12]

S. L. Sobolev,Applications of functional analysis in mathematical physics, Amer. Math. Soc. (1963). 10.1090/mmono/007

[13]

L. C. Young,Partial area, Rivista Mat. Univ. Parma,10 (1959).

Cited By

1,451

Quantitative Inequalities for the Expected Lifetime of Brownian Motion

Daesung Kim · 2021

Michigan Mathematical Journal

Global regularity for solutions of the Navier–Stokes equation sufficiently close to being eigenfunctions of the Laplacian

Evan Miller · 2021

Proceedings of the American Mathema...

Solvability of a critical semilinear problem with the spectral Neumann fractional Laplacian

N. Ustinov · 2021

St. Petersburg Mathematical Journal

High energy sign-changing solutions for Coron's problem

Shengbing Deng, Monica Musso · 2021

Journal of Differential Equations

The effect of curvature in fractional Hardy–Sobolev inequality involving the spectral Dirichlet Laplacian

Nikita Ustinov · 2020

Transactions of the American Mathem...

Infinite lattice models by an expansion with a non-Gaussian initial approximation

Aleksandr Ivanov, Vasily Sazonov · 2019

Physics Letters B

Absence of Global Solutions of a Mixed Problem for a Schrödinger-Type Nonlinear Evolution Equation

Sh. M. Nasibov · 2018

Theoretical and Mathematical Physic...

Sign-changing blowing-up solutions for supercritical Bahri–Coron’s problem

Monica Musso, Juncheng Wei · 2016

Calculus of Variations and Partial...

Dynamics Near the Ground State for the Energy Critical Nonlinear Heat Equation in Large Dimensions

Charles Collot, Frank Merle · 2016

Communications in Mathematical Phys...

Optimal estimates for fractional fast diffusion equations

Juan Luis Vázquez, Bruno Volzone · 2015

Journal de Mathématiques Pures et A...

Nondegeneracy of Nodal Solutions to the Critical Yamabe Problem

Monica Musso, Juncheng Wei · 2015

Communications in Mathematical Phys...

Existence and symmetry of positive ground states for a doubly critical Schrödinger system

Zhijie Chen, Wenming Zou · 2014

Transactions of the American Mathem...

On the Caffarelli–Kohn–Nirenberg-type inequalities involving critical and supercritical weights

Toshio Horiuchi, Peter Kumlin · 2012

Kyoto Journal of Mathematics

The effect of the domain topology on the number of minimal nodal solutions of an elliptic equation at critical growth in a symmetric domain

Alfonso Castro, M nica Clapp · 2003

Nonlinearity

On the Symmetry of Extremals in the Weight Embedding Theorem

A. I. Nazarov · 2001

Journal of Mathematical Sciences

The best constant problem in the Sobolev embedding theorem for complete Riemannian manifolds

Emmanuel Hebey, Michel Vaugon · 1995

Duke Mathematical Journal

The Yamabe problem

John M. Lee, Thomas H. Parker · 1987

Bulletin of the American Mathematic...

Conformal complete metrics with prescribed non-negative Gaussian curvature in ?2

Patricio Aviles · 1986

Inventiones mathematicae

Some existence results for superlinear elliptic boundary value problems involving critical exponents

G Cerami, S Solimini · 1986

Journal of Functional Analysis

Sobolev inequalities with remainder terms

Haïm Brezis, Elliott H. Lieb · 1985

Journal of Functional Analysis

Metrics

1,451

Citations

13

References

Details

Published: Dec 01, 1976
Vol/Issue: 110(1)
Pages: 353-372
License: View

Authors

G

Giorgio Talenti

Cite This Article

Giorgio Talenti (1976). Best constant in Sobolev inequality. Annali di Matematica Pura ed Applicata, 110(1), 353-372. https://doi.org/10.1007/bf02418013

Best constant in Sobolev inequality

You May Also Like