ASYMPTOTIC PROFILE FOR THE SUB-EXTREMALS OF THE SHARP SOBOLEV INEQUALITY ON THE SPHERE

DOI10.1081/PDE-100002377zbMath0998.58010MaRDI QIDQ2747893

Frédéric Robert, Olivier Druet

Publication date: 14 October 2001

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

zbMATH Keywords

sharp Sobolev inequalitysub-extremal functions

Mathematics Subject Classification ID

Variational inequalities (global problems) in infinite-dimensional spaces (58E35)

Related Items (4)

Optimal constants in the exceptional case of Sobolev inequalities on Riemannian manifolds ⋮ A 𝐶⁰-theory for the blow-up of second order elliptic equations of critical Sobolev growth ⋮ Best constants in the exceptional case of Sobolev inequalities ⋮ Elliptic equations with critical Sobolev exponents in dimension 3

Cites Work

• Proof of two conjectures of H. Brezis and L. A. Peletier
• Elliptic equations with nearly critical growth
• Nonlinear elliptic equations on compact Riemannian manifolds and asymptotics of Emden equations
• Blow-up behavior of ground states of semilinear elliptic equations in \(R^ n\) involving critical Sobolev exponents
• Best constant in Sobolev inequality
• Extremal functions for an optimal Sobolev inequality in the conformal class of the sphere
• The best constants problem in Sobolev inequalities
• Prescribing scalar curvature on \(\mathbb{S}^ n\) and related problems. I
• The best constant problem in the Sobolev embedding theorem for complete Riemannian manifolds
• Prescribed scalar curvature on the \(n\)-sphere
• Asymptotic symmetry and local behavior of semilinear elliptic equations with critical sobolev growth
• Global and local behavior of positive solutions of nonlinear elliptic equations
• The principal eigenvalue and maximum principle for second‐order elliptic operators in general domains

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