Exotic solutions of the conformal scalar curvature equation in n
Annales de l'I.H.P. Analyse non linéaire, Tome 18 (2001) no. 3, p. 297-307
@article{AIHPC_2001__18_3_297_0,
     author = {Leung, Man Chun},
     title = {Exotic solutions of the conformal scalar curvature equation in $\mathbb {R}^n$},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Elsevier},
     volume = {18},
     number = {3},
     year = {2001},
     pages = {297-307},
     zbl = {0986.35033},
     language = {en},
     url = {http://http://www.numdam.org/item/AIHPC_2001__18_3_297_0}
}
Leung, Man Chun. Exotic solutions of the conformal scalar curvature equation in $\mathbb {R}^n$. Annales de l'I.H.P. Analyse non linéaire, Tome 18 (2001) no. 3, pp. 297-307. http://www.numdam.org/item/AIHPC_2001__18_3_297_0/

[1] Bahri A, Coron J, The scalar-curvature problem on standard three-dimensional sphere, J. Func. Anal. 95 (1991) 106-172. | MR 1087949 | Zbl 0722.53032

[2] Caffarelli L, Gidas B, Spruck J, Asymptotic symmetry and local behavior of semilinear elliptic equations with critical Sobolev growth, Comm. Pure Appl. Math. 42 (1989) 271-297. | MR 982351 | Zbl 0702.35085

[3] Chang K.-C, Liu J.-Q, On Nirenberg's problem, Internat. J. Math. 4 (1993) 35-58. | MR 1209959 | Zbl 0786.58010

[4] Chang S.-Y, Yang P, A perturbation result in prescribing scalar curvature on Sn, Duke Math. J. 64 (1991) 27-69. | MR 1131392 | Zbl 0739.53027

[5] Chen C.-C, Lin C.-S, On compactness and completeness of conformal metrics in RN, Asian J. Math. 1 (1997) 549-559. | MR 1604918 | Zbl 0901.53027

[6] Chen C.-C, Lin C.-S, Estimates of the conformal scalar curvature equation via the method of moving planes, Comm. Pure Appl. Math. 50 (1997) 971-1019. | MR 1466584 | Zbl 0958.35013

[7] Chen C.-C, Lin C.-S, Estimates of the conformal scalar curvature equation via the method of moving planes. II, J. Differential Geom. 49 (1998) 115-178. | MR 1642113 | Zbl 0961.35047

[8] Chen C.-C, Lin C.-S, On the asymptotic symmetry of singular solutions of the scalar curvature equations, Math. Ann. 313 (1999) 229-245. | MR 1679784 | Zbl 0927.35034

[9] Chen W.-X, Li C.-M, A necessary and sufficient condition for the Nirenberg problem, Comm. Pure Appl. Math. 48 (1995) 657-667. | MR 1338474 | Zbl 0830.35034

[10] Cheung K.-L, Leung M.-C, Asymptotic behavior of positive solutions of the equation Δu+Ku(n+2)/(n−2)=0 in Rn and positive scalar curvature, in: Discrete Contin. Dynam. Systems, Added Volume, Proceedings of the International Conference on Dynamical Systems and Differential Equations, 2001, pp. 109-120.

[11] Delaunay C, Sur la surface de revolution dont la courbure moyenne est constante, J. de Mathématiques 6 (1841) 309-320.

[12] Ding W.-Y, Ni W.-M, On the elliptic equation Δu+Ku(n+2)/(n−2)=0 and related topics, Duke Math. J. 52 (1985) 485-506. | Zbl 0592.35048

[13] Fowler R, Further studies of Emden's and similar differential equations, Quart. J. Math. Oxford Ser. 2 (1931) 259-288. | Zbl 0003.23502

[14] Gidas B, Ni W.-M, Nirenberg L, Symmetry and related properties via the maximum principle, Comm. Math. Phys. 68 (1979) 209-243. | MR 544879 | Zbl 0425.35020

[15] Gidas B, Ni W.-M, Nirenberg L, Symmetry of positive solutions of nonlinear elliptic equations in Rn, in: Mathematical Analysis and Applications, Part A, Adv. in Math. Suppl. Stud., 7a, Academic Press, New York, 1981, pp. 369-402. | MR 634248 | Zbl 0469.35052

[16] Korevaar N, Mazzeo R, Pacard F, Schoen R, Refined asymptotics for constant scalar curvature metrics with isolated singularities, Invent. Math. 135 (1999) 233-272. | MR 1666838 | Zbl 0958.53032

[17] Leung M.-C, Conformal scalar curvature equations on complete manifolds, Comm. Partial Differential Equations 20 (1995) 367-417. | MR 1318076 | Zbl 0833.53038

[18] Leung M.-C, Asymptotic behavior of positive solutions of the equation Δgu+Kup=0 in a complete Riemannian manifold and positive scalar curvature, Comm. Partial Differential Equations 24 (1999) 425-462. | Zbl 0939.58024

[19] Leung M.-C., Growth estimates on positive solutions of the equation Δu+Ku(n+2)/(n−2)=0 in Rn, Canad. Math. Bull., to appear. | Zbl 0979.35046

[20] Li Y.-Y, Prescribing scalar curvature on Sn and related problems, part I, J. Differential Equations 120 (1995) 319-410. | MR 1347349 | Zbl 0827.53039

[21] Li Y.-Y, Prescribing scalar curvature on Sn and related problems, part II: existence and compactness, Comm. Pure Appl. Math. 49 (1996) 541-597. | MR 1383201 | Zbl 0849.53031

[22] Lin C.-S, Estimates of the conformal scalar curvature equation via the method of moving planes III, Comm. Pure Appl. Math. 53 (2000) 611-646. | MR 1737506 | Zbl 1035.53052

[23] Loewner C, Nirenberg L, Partial differential equations invariant under conformal or projective transformations, in: Contributions to Analysis (a collection of papers dedicated to Lipman Bers), Academic Press, New York, 1974, pp. 245-272. | MR 358078 | Zbl 0298.35018

[24] Mazzeo R, Pacard F, Constant scalar curvature metrics with isolated singularities, Duke Math. J. 99 (1999) 353-418. | MR 1712628 | Zbl 0945.53024

[25] Mazzeo R, Pollack D, Uhlenbeck K, Moduli spaces of singular Yamabe metrics, J. Amer. Math. Soc. 9 (1996) 303-344. | MR 1356375 | Zbl 0849.58012

[26] Schoen R, The existence of weak solutions with prescribed singular behavior for a conformally invariant scalar equation, Comm. Pure Appl. Math. 41 (1988) 317-392. | MR 929283 | Zbl 0674.35027

[27] Taliaferro S, On the growth of superharmonic functions near an isolated singularity, I., J. Differential Equations 158 (1999) 28-47. | MR 1721720 | Zbl 0939.31005