A few symmetry results for nonlinear elliptic PDE on noncompact manifolds
Annales de l'I.H.P. Analyse non linéaire, Volume 19 (2002) no. 3, p. 313-342
@article{AIHPC_2002__19_3_313_0,
     author = {Almeida, Lu\'\i s and Damascelli, Lucio and Ge, Yuxin},
     title = {A few symmetry results for nonlinear elliptic PDE on noncompact manifolds},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Elsevier},
     volume = {19},
     number = {3},
     year = {2002},
     pages = {313-342},
     zbl = {1029.35096},
     mrnumber = {1956953},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2002__19_3_313_0}
}
Almeida, Luís; Damascelli, Lucio; Ge, Yuxin. A few symmetry results for nonlinear elliptic PDE on noncompact manifolds. Annales de l'I.H.P. Analyse non linéaire, Volume 19 (2002) no. 3, pp. 313-342. http://www.numdam.org/item/AIHPC_2002__19_3_313_0/

[1] Alexandrov A., Uniqueness theorem for surfaces in the large, Vestnik Leningrad Univ. Math. 11 (1956) 5-17. | MR 86338

[2] Almeida L., Ge Y., Symmetry results for positive solutions of some elliptic equations on manifolds, Annals Global Anal. Geom. 18 (2000) 153-170. | MR 1744588 | Zbl 0968.58015

[3] Berestycki H., Caffarelli L.A., Nirenberg L., Symmetry for elliptic equations in a half space, in: Boundary Value Problems for Partial Differential Equations and Applications, RMA Res. Notes Appl. Math., 29, Masson, Paris, 1993, pp. 27-42. | MR 1260436 | Zbl 0793.35034

[4] Berestycki H., Caffarelli L.A., Nirenberg L., Inequalities for second order elliptic equations with applications to unbounded domains. I, Duke Math. J. 81 (1996) 467-494. | MR 1395408 | Zbl 0860.35004

[5] Berestycki H., Caffarelli L.A., Nirenberg L., Monotonicity for elliptic equations in unbounded Lipshitz domains, Comm. Pure Appl. Math. 50 (1997) 1089-1111. | MR 1470317 | Zbl 0906.35035

[6] Berestycki H., Caffarelli L.A., Nirenberg L., Further qualitative properties for elliptic equations in unbounded domains, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 25 (1997) 69-94. | Numdam | MR 1655510 | Zbl 1079.35513

[7] Berestycki H., Nirenberg L., On the method of moving planes and the sliding method, Bol. Soc. Bras. Mat. 22 (1991) 1-39. | MR 1159383 | Zbl 0784.35025

[8] Damascelli L., Pacella F., Ramaswamy M., Symmetry of ground states of p-Laplace equations via the moving plane method, Arch. Ration. Mech. Anal. 148 (1999) 291-308. | MR 1716666 | Zbl 0937.35050

[9] Damascelli L., Ramaswamy M., Symmetry of C1 solutions of p-Laplace equations in RN, Advanced Nonlinear Studies 1 (2001) 40-64. | MR 1850203 | Zbl 0998.35016

[10] 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

[11] Gidas B., Ni W.M., Nirenberg L., Symmetry of positive solutions of nonlinear elliptic equations in RN, Adv. Math., Suppl. Stud. 7A (1981) 369-402. | MR 634248 | Zbl 0469.35052

[12] Hebey E., Introduction à l'analyse non linéaire sur les variétés, Fondations, Diderot Editeur, Paris, 1997. | Zbl 0918.58001

[13] Hebey E., Sobolev Spaces on Riemannian Manifolds, Lecture Notes in Mathematics, 1635, Springer-Verlag, Berlin, 1996. | MR 1481970 | Zbl 0866.58068

[14] Li C., Monotonicity and symmetry of solutions of fully nonlinear elliptic equations on unbounded domains, Comm. Partial Differential Equations 16 (1991) 585-615. | MR 1113099 | Zbl 0741.35014

[15] Li Y., Ni W.M., Radial symmetry of positive solutions of nonlinear elliptic equations in RN, Comm. Partial Differential Equations 18 (1993) 1043-1054. | MR 1218528 | Zbl 0788.35042

[16] Serrin J., A symmetry problem in potential theory, Arch. Ration. Mech. Anal. 43 (1971) 304-318. | MR 333220 | Zbl 0222.31007

[17] Serrin J., Zou H., Symmetry of ground states of quasilinear elliptic equations, Arch. Ration. Mech. Anal. 148 (1999) 265-290. | MR 1716665 | Zbl 0940.35079

[18] Terracini S., Symmetry properties of positive solutions to some elliptic equations with nonlinear boundary conditions, Differential Integral Equations 8 (1995) 1911-1922. | MR 1348957 | Zbl 0835.35055

[19] Terracini S., On positive entire solutions to a class of equations with a singular coefficient and critical exponent, Adv. Differential Equations 1 (1996) 241-264. | MR 1364003 | Zbl 0847.35045