Exotic solutions of the conformal scalar curvature equation in $\mathbb {R}^n$

Leung, Man Chun

Exotic solutions of the conformal scalar curvature equation in

ℝ^{n}

Leung, Man Chun

Annales de l'I.H.P. Analyse non linéaire, Tome 18 (2001) no. 3, pp. 297-307.

Zbl

@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},
     pages = {297--307},
     publisher = {Elsevier},
     volume = {18},
     number = {3},
     year = {2001},
     zbl = {0986.35033},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2001__18_3_297_0/}
}

TY  - JOUR
AU  - Leung, Man Chun
TI  - Exotic solutions of the conformal scalar curvature equation in $\mathbb {R}^n$
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2001
SP  - 297
EP  - 307
VL  - 18
IS  - 3
PB  - Elsevier
UR  - http://www.numdam.org/item/AIHPC_2001__18_3_297_0/
LA  - en
ID  - AIHPC_2001__18_3_297_0
ER  -

%0 Journal Article
%A Leung, Man Chun
%T Exotic solutions of the conformal scalar curvature equation in $\mathbb {R}^n$
%J Annales de l'I.H.P. Analyse non linéaire
%D 2001
%P 297-307
%V 18
%N 3
%I Elsevier
%U http://www.numdam.org/item/AIHPC_2001__18_3_297_0/
%G en
%F 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/

Bibliographie
Cité par

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

[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 | Zbl

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

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

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

[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 | Zbl

[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 | Zbl

[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 | Zbl

[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 | Zbl

[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

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

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

[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 | Zbl

[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 | Zbl

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

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

[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

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

[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 | Zbl

[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 | Zbl

[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 | Zbl

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

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

[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 | Zbl

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