Advances in Differential Equations

Second-best constant and extremal functions in Sobolev inequalities in the presence of symmetries

Zoé Faget

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Abstract

We prove results on the existence of extremal functions for critical Sobolev inequalities on Riemannian manifolds when the functions are invariant under an isometry group. In order to get those results, we study precisely a concentration phenomenon around an orbit for a sequence of solutions of a nonlinear PDE invariant under the isometry group.

Article information

Source
Adv. Differential Equations Volume 9, Number 7-8 (2004), 745-770.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355867923

Mathematical Reviews number (MathSciNet)
MR2100394

Zentralblatt MATH identifier
1100.58010

Subjects
Primary: 58J05: Elliptic equations on manifolds, general theory [See also 35-XX]
Secondary: 26D15: Inequalities for sums, series and integrals 35B40: Asymptotic behavior of solutions 35J60: Nonlinear elliptic equations 46E35: Sobolev spaces and other spaces of "smooth" functions, embedding theorems, trace theorems

Citation

Faget, Zoé. Second-best constant and extremal functions in Sobolev inequalities in the presence of symmetries. Adv. Differential Equations 9 (2004), no. 7-8, 745--770. https://projecteuclid.org/euclid.ade/1355867923.


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