On Liouville theorem and apriori estimates for the scalar curvature equations
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 27 (1998) no. 1, pp. 107-130.
@article{ASNSP_1998_4_27_1_107_0,
author = {Lin, Chang-Shou},
title = {On {Liouville} theorem and apriori estimates for the scalar curvature equations},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
pages = {107--130},
publisher = {Scuola normale superiore},
volume = {Ser. 4, 27},
number = {1},
year = {1998},
zbl = {0974.53032},
mrnumber = {1658881},
language = {en},
url = {http://www.numdam.org/item/ASNSP_1998_4_27_1_107_0/}
}
TY  - JOUR
AU  - Lin, Chang-Shou
TI  - On Liouville theorem and apriori estimates for the scalar curvature equations
JO  - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY  - 1998
DA  - 1998///
SP  - 107
EP  - 130
VL  - Ser. 4, 27
IS  - 1
PB  - Scuola normale superiore
UR  - http://www.numdam.org/item/ASNSP_1998_4_27_1_107_0/
UR  - https://zbmath.org/?q=an%3A0974.53032
UR  - https://www.ams.org/mathscinet-getitem?mr=1658881
LA  - en
ID  - ASNSP_1998_4_27_1_107_0
ER  - 
%0 Journal Article
%A Lin, Chang-Shou
%T On Liouville theorem and apriori estimates for the scalar curvature equations
%J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
%D 1998
%P 107-130
%V Ser. 4, 27
%N 1
%I Scuola normale superiore
%G en
%F ASNSP_1998_4_27_1_107_0
Lin, Chang-Shou. On Liouville theorem and apriori estimates for the scalar curvature equations. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 27 (1998) no. 1, pp. 107-130. http://www.numdam.org/item/ASNSP_1998_4_27_1_107_0/

[1] A. Bahri - J. C, The scalar curvature problem on three-dimensional sphere, J. Funct. Anal. 95 (1991), 106-172. | MR | Zbl

[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. | MR | Zbl

[3] S.Y. Chang - M.J. Gursky - P. Yang, The scalar curvature equation on 2 and 3-splere, Calc. Var. Partial Differential Equations 1 (1993), 205-229. | MR | Zbl

[4] W. Chen - C. Li, Classification of solutions of some nonlinear elliptic equations, Duke Math. J. 63 (1991), 615-622. | MR | Zbl

[5] W. Chen - C. Li, Apriori estimates for prescribing scalar curvature equations, Ann. of Math. (2) 145 (1997), 547-564. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[8] J. Escobar - R. Schoen, Conformal metric with prescribed scalar curvature, Invent. Math. 86 (1986), 243-254. | MR | Zbl

[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. | Zbl

[10] Y.Y. Li, On - Δu = K(x)u5 in R3, Comm. Pure Appl. Math. 46 (1993), 303-340.

[11] Y.Y. Li, Prescribing scalar curvature on Sn and related problems, Part I. J. Differential equations 120 (1995), 319-410. | MR | Zbl

[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. | MR | Zbl

[13] Y.Y. Li - M.J. Zhu, Uniqueness theorems through the method of moving sphere, Duke Math. J. 80 (1995), 383-417. | MR | Zbl

[14] C.S. Lin, Liouville-type theorems for semilinear elliptic equations involving the Sobolev exponent, Math. Z., 228 (1998), 723-744. | MR | Zbl

[15] L. Nirenberg, "Topics in nonlinear functional analysis", Lecture notes, Courant Institute, New York University, 1974. | MR | Zbl

[16] P. Padilla, "On some nonlinear elliptic problems", Dissertations, New York University, 1994.

[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. | MR | Zbl

[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. | MR | Zbl

[19] J. Serrin, A symmetry problem in potential theory, Arch. Rational Mech. Anal. 43 (1971), 304-318. | MR | Zbl

[20] R. Schoen - D. Zhang, Prescribed Scalar Curvature on the n-sphere, Calc. Var. Partial Differential Equations 4 (1996), 1-25. | MR | Zbl