Meilleures constantes dans le théorème d’inclusion de Sobolev

Hebey, Emmanuel; Vaugon, Michel

doi:10.1016/s0294-1449(16)30097-x

Cited by 99 publications

(83 citation statements)

References 16 publications

(10 reference statements)

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“…T. Aubin's theorem has been improved by E. Hebey and M.Vaugon ( [9], [10], ) who showed that the ǫ in Theorem 1.4 can be removed, in both compact and complete settings.…”

Section: Introductionmentioning

confidence: 99%

Remarks on the Extension of the Ricci Flow

2012

J Geom Anal

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“…T. Aubin's theorem has been improved by E. Hebey and M.Vaugon ( [9], [10], ) who showed that the ǫ in Theorem 1.4 can be removed, in both compact and complete settings.…”

Section: Introductionmentioning

confidence: 99%

Remarks on the Extension of the Ricci Flow

2012

J Geom Anal

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“…A different aspect of critical Sobolev inequalities has been investigated by Hebey and Vaugon [13]. On a general Riemannian manifold (M, g) one has…”

mentioning

confidence: 99%

Green’s function, harmonic transplantation, and best Sobolev constant in spaces of constant curvature

Bandle¹,

Brillard

Flucher³

1998

Trans. Amer. Math. Soc.

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Abstract. We extend the method of harmonic transplantation from Euclidean domains to spaces of constant positive or negative curvature. To this end the structure of the Green's function of the corresponding LaplaceBeltrami operator is investigated. By means of isoperimetric inequalities we derive complementary estimates for its distribution function. We apply the method of harmonic transplantation to the question of whether the best Sobolev constant for the critical exponent is attained, i.e. whether there is an extremal function for the best Sobolev constant in spaces of constant curvature. A fairly complete answer is given, based on a concentration-compactness argument and a Pohozaev identity. The result depends on the curvature.

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“…It is well known that the best constant A in this inequality is A = K(n, 2) 2 = 4 n(n − 2)ω 2 n n where ω n stands for the volume of the standard n-dimensional sphere. As shown by Hebey and Vaugon [6], this best constant is attained. In other 1 words, there exists B > 0 such that S(K(n, 2) 2 , B) is true for all u ∈ H 2 1 (M).…”

Section: Critical Functionsmentioning

confidence: 56%