Positive solutions for a fourth order equation invariant under isometries
作者： Frédéric Robert
DOI: 10.1090/S0002-9939-02-06676-5
关键词:
摘要: Let (M, g) be a smooth compact Riemannian manifold of dimension n > 5. We consider the problem (*) Δ 2 g u + αΔ au =fu, where = -divg(⊇), α,α ∈ R, u, f E C∞(M). require to positive and invariant under isometries. prove existence results for on arbitrary manifolds. This includes case geometric Paneitz-Branson operator sphere.
ams.org
sci-hub.se 参考文章(8)
Neil S Trudinger, David G Gilbarg, Elliptic Partial Differential Equations of Second Order ,(2018)
Michel Ledoux, Emmanuel Hebey, Zindine Djadli, Paneitz-type operators and applications Duke Mathematical Journal. ,vol. 104, pp. 129- 169 ,(2000) , 10.1215/S0012-7094-00-10416-4
Jose F. Escobar, Richard M. Schoen, Conformal metrics with prescribed scalar curvature Inventiones Mathematicae. ,vol. 86, pp. 243- 254 ,(1986) , 10.1007/BF01389071
Olivier Druet, THE BEST CONSTANTS PROBLEM IN SOBOLEV INEQUALITIES Mathematische Annalen. ,vol. 314, pp. 327- 346 ,(1999) , 10.1007/S002080050297
Thomas P Branson, Group representations arising from Lorentz conformal geometry Journal of Functional Analysis. ,vol. 74, pp. 199- 291 ,(1987) , 10.1016/0022-1236(87)90025-5
D. E. Edmunds, D. Fortunato, E. Jannelli, Critical exponents, critical dimensions and the biharmonic operator Archive for Rational Mechanics and Analysis. ,vol. 112, pp. 269- 289 ,(1990) , 10.1007/BF00381236
Emmanuel Hebey, Frédéric Robert, Coercivity and Struwe's compactness for Paneitz type operators with constant coefficients Calculus of Variations and Partial Differential Equations. ,vol. 13, pp. 491- 517 ,(2001) , 10.1007/S005260100084
J. MOSER, On a Nonlinear Problem in Differential Geometry Dynamical Systems#R##N#Proceedings of a Symposium Held at the University of Bahia, Salvador, Brasil, July 26–august 14, 1971. pp. 273- 280 ,(1973) , 10.1016/B978-0-12-550350-1.50026-6