✦ LIBER ✦
Best constants for supercritical Sobolev inequalities and application to some quasilinear supercritical elliptic equations of scalar curvature type
✍ Scribed by Dimitris Iliopoulos
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- French
- Weight
- 115 KB
- Volume
- 124
- Category
- Article
- ISSN
- 0007-4497
No coin nor oath required. For personal study only.
✦ Synopsis
Let Σ be the set of O(k) × O(m)-invariant functions on the unit sphere S n , k + m = n + 1, k m 2. We investigate the optimal value of the constant B in the inequality
where u ∈ H q 1 (S n ) ∩ Σ and 1/p = 1/q -1/k. We then give an application to the existence of positive solutions to scalar curvature type equations with critical supercritical Sobolev growth.