A spherical Harnack inequality for singular solutions of nonlinear elliptic equations

Chen, Chiun-Chuan; Lin, Chang-Shou

Chen, Chiun-Chuan ; Lin, Chang-Shou

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 30 (2001) no. 3-4, pp. 713-738.

MR Zbl

@article{ASNSP_2001_4_30_3-4_713_0,
     author = {Chen, Chiun-Chuan and Lin, Chang-Shou},
     title = {A spherical {Harnack} inequality for singular solutions of nonlinear elliptic equations},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {713--738},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 30},
     number = {3-4},
     year = {2001},
     mrnumber = {1896083},
     zbl = {1072.35071},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2001_4_30_3-4_713_0/}
}

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Chen, Chiun-Chuan; Lin, Chang-Shou. A spherical Harnack inequality for singular solutions of nonlinear elliptic equations. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 30 (2001) no. 3-4, pp. 713-738. http://www.numdam.org/item/ASNSP_2001_4_30_3-4_713_0/

Bibliographie
Cité par

[1] G. Bianchi, Nonexistence of positive solutions to semilinear elliptic equations on Rn or Rn+ through the method of moving planes, Comm. Partial Differential Equation 22 (1997), 1671-1670. | MR | Zbl

[2] H. Brezis - Y.Y. Li - I. Shafrir, A sup + inf inequality for some nonlinear elliptic equations involving exponential nonlinearities, J. Func. Anal. 115 (1993), 34.4.-358. | MR | Zbl

[3] 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

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

[5] C.C. Chen - C.S. Lin, Local behavior of singular positive solutions of semilinear elliptic equations with Sobolev exponent, Duke Math. J., 78 (1995), 315-334. | MR | Zbl

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

[7] C.C. Chen - C.S. Lin, Estimates of the conformal scalar curvature equation via the method of moving planes, Comm. Pure Appl. Math. 50 (1997), 971-1017. | MR | Zbl

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

[9] B. Gidas - W.M. Ni - L. Nirenberg, Symmetry of positive solutions of nonlinear equations in Rn, In: "Mathematical Analysis and Applications", part A, pp. 369-402, Advances in Math. Supp. Stud. 79, Academic Press, New York-London, 1981. | Zbl

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

[11] C. Li, Local asymptotic symmetry of Singular Solutions to Nonlinear Elliptic Equations, Invent. Math. 123 (1996), 221-232. | MR | Zbl

[12] Y.Y. Li, Harnack type inequality: the method of moving planes, Comm. Math. Phys. 200 (1999), 421-444. | MR | Zbl

[13] C.S. Lin, On Liouville theorem and apriori estimate for the scalar curvature equations, Ann. Scuola. Norm. Sup. Pisa Cl. Sci. (4) 27 (1998), 107-130. | Numdam | MR | Zbl

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

[15] R. Mazzeo - F. Pacard, A construction of singular solutions for semilinear elliptic equation using asymptotic analysis, J. Differential Geom. 44 (1996), 331-370. | MR | Zbl

[16] D. Pollack, Compactness results for complete metrics of constant positive scalar curvature on of subdomains of Sn' Indiana Univ. Math. J. 42 (1993), 1441-1456. | MR | Zbl

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

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

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