On Liouville theorem and apriori estimates for the scalar curvature equations

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1. [1] A. Bahri - J. C, The scalar curvature problem on three-dimensional sphere, J. Funct. Anal.95 (1991), 106-172. Zbl0722.53032MR1087949
2. [2] L.A. Caffarelli - B. Gidas - J. Spruck, Asymptotic Symmetry and local behavior of semilinear elliptic equations with critical Sobolev exponent, Comm. Pure Appl. Math.42 (1989), 271-297. Zbl0702.35085MR982351
3. [3] S.Y. Chang - M.J. Gursky - P. Yang, The scalar curvature equation on 2 and 3-splere, Calc. Var. Partial Differential Equations1 (1993), 205-229. Zbl0822.35043MR1261723
4. [4] W. Chen - C. Li, Classification of solutions of some nonlinear elliptic equations, Duke Math. J.63 (1991), 615-622. Zbl0768.35025MR1121147
5. [5] W. Chen - C. Li, Apriori estimates for prescribing scalar curvature equations, Ann. of Math. (2) 145 (1997), 547-564. Zbl0877.35036MR1454703
6. [6] C.C. Chen - C.S. Lin, Estimates of the conformal scalar curvature equations via the method of moving planes, Comm. Pure Appl. Math.50 (1997), 971-1017. Zbl0958.35013MR1466584
7. [7] C.C. Chen - C.S. Lin, Estimates of the conformal scalar curature equations via the method of moving planes, II, J. Differential Geom., 49 (1998), 115-178. Zbl0961.35047MR1642113
8. [8] J. Escobar - R. Schoen, Conformal metric with prescribed scalar curvature, Invent. Math.86 (1986), 243-254. Zbl0628.53041MR856845
9. [9] B. Gidas - W.M. Ni- L. Nirenberg, Symmetry of positive solutions of nonlinear equations in Rn, Analysis and Applications, part A, 369-402, Advances in Math. Supp. Stud. 79, Academic Press, New York- London, 1981. Zbl0469.35052
10. [10] Y.Y. Li, On - Δu = K(x)u5 in R3, Comm. Pure Appl. Math.46 (1993), 303-340. 
11. [11] Y.Y. Li, Prescribing scalar curvature on Sn and related problems, Part I. J. Differential equations120 (1995), 319-410. Zbl0827.53039MR1347349
12. [12] Y.Y. Li, Prescribing scalar curvature on Sn and related problems, Part II: Existence and compactness, Comm. Pure Appl. Math.49 (1996), 541-597. Zbl0849.53031MR1383201
13. [13] Y.Y. Li - M.J. Zhu, Uniqueness theorems through the method of moving sphere, Duke Math. J.80 (1995), 383-417. Zbl0846.35050MR1369398
14. [14] C.S. Lin, Liouville-type theorems for semilinear elliptic equations involving the Sobolev exponent, Math. Z., 228 (1998), 723-744. Zbl0915.35036MR1644448
15. [15] L. Nirenberg, "Topics in nonlinear functional analysis", Lecture notes, Courant Institute, New York University, 1974. Zbl0286.47037MR488102
16. [16] P. Padilla, "On some nonlinear elliptic problems", Dissertations, New York University, 1994. 
17. [17] D. Pollack, Compactness results for complete metrics of constant positive Scalar curvature on subdomains of Sn, Indiana Univ. Math. J.42 (1993), 1441-1456. Zbl0794.53025MR1266101
18. [18] R. Schoen, Variational theory for the total scalar curvature functional for Riemannian metrics and related topics, in Topics in Calculus of Variations, Lecture notes in Mathematics, No. 1365, edited by M. Giaquinta, Springer-Verlag, 1989, 20-154. Zbl0702.49038MR994021
19. [19] J. Serrin, A symmetry problem in potential theory, Arch. Rational Mech. Anal.43 (1971), 304-318. Zbl0222.31007MR333220
20. [20] R. Schoen - D. Zhang, Prescribed Scalar Curvature on the n-sphere, Calc. Var. Partial Differential Equations4 (1996), 1-25. Zbl0843.53037MR1379191

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