Advances in Differential Equations
- Adv. Differential Equations
- Volume 9, Number 7-8 (2004), 745-770.
Second-best constant and extremal functions in Sobolev inequalities in the presence of symmetries
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.
Adv. Differential Equations, Volume 9, Number 7-8 (2004), 745-770.
First available in Project Euclid: 18 December 2012
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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
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