A priori estimates for solutions of "sub-critical" equations on CR sphere

Advanced Nonlinear Studies

Volumn 3, Issue 3, 2003, Pages 355-395

  Prajapat, J ^a   Ramaswamy, Mythily ^b  

^a INDIAN STATISTICAL INSTITUTE   (India)

^b TATA INSTITUTE OF FUNDAMENTAL RESEARCH   (India)

Author keywords

Apriori estimate; CR sphere; Critical exponent; Subelliptic operator

Indexed keywords

EID: 24944470669     PISSN: 15361365     EISSN: None     Source Type: Journal    
DOI: 10.1515/ans-2003-0303     Document Type: Article

References (15)

1. J.M. Bony, Principe du Maximum, Inégalité de Harnack et unicité du problèe de Cauchy pour les operateua elliptiques dégénérés, Ann. Inst. Fourier Grenobles 19 (1969), no.1, 277-304.
2. GC. Chen and C-S. Lin, Estimates of the conformal scalar curvature equation via the method of moving planes, Comm. pure and Appl. Math. 50 (1997), no.10, 971-1017. (Pubitemid 127383426)
3. W. Chen and C. Li, A priori estimates for prescribing scalar curvature equations, Ann. of Math. (2) 145 (1997), 110.3, 547-564.
4. N. Garofalo, E. Lanconelli, Existence and nonexistence results for semilinear equations on the Heisenberg group, Indiana University Jr. 41 (1992), no.1, 71-98.
5. G. Citti, N. Garofalo and E. Lanconelli, Harnack's znequaltiy for sum of squares of vector fields plw a potential, American J. of Math. 115 (1993), 699-734.
6. G.B. Folland, Subelliptic estimates and function spaces on nilpotent Lie groups, Arkiv für Math. 1 (1975), no.3, 161-207.
7. G.B. Folland and E.M. Stein, Estimates for the∂b complex and analysis on the Heisenberg p u p, Comm. in Pure and Applied Math. 37 (1974), 429-522.
8. L. Hormander, Hypoelliptic second order diitewntial equations, Acta Math. 119 (1967), 147-171.
9. D. Jerison, J.M. Lee, The Yamabe Problem on CR manifololds, J. Differential Geometry 2 (1987), 167-197.
10. D. Jerison, J.M. Lee, Extremals for the Sobolev Inequality on the Heisenberg group and the CR Yamde Problepn, J. of Amer. Math. Soc. 1 (1988), no.1, 1-13.
11. A. Koráyi and S. Vági, Cauchy-Szegö integrals for systems of harmonic functions, Ann. Scuola Norm. Sup. Pisa (3) 26 (1972), 181-196.
12. R. Schoen, D. Zhang, Prescribed scalar curvature on the n-sphere, Calc. of Var. Partial Differential Equations 4 (1996), no.1, 1-25. (Pubitemid 126488485)
13. n and related problems, Part 1, J. of Differential Equations 120 (1995), no.2, 319-410.
14. N.Th. Varopoulos, L.S. Coste and T. Coulhon, Analysis and Geometry on groups, Cambridge University Press, 1992.
15. N.Th. Varopoulos, Fonctions harmoniques sur les groupes de Lie, C.R.Acad.Sci.Paris Sér I Math. 304 (1987), no.17, 519-521.