Inheritance of symmetry for positive solutions of semilinear elliptic boundary value problems
Kawohl, Bernd ; Sweers, Guido
Annales de l'I.H.P. Analyse non linéaire, Tome 19 (2002), p. 705-714 / Harvested from Numdam
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Publié le : 2002-01-01
@article{AIHPC_2002__19_5_705_0,
     author = {Kawohl, Bernd and Sweers, Guido},
     title = {Inheritance of symmetry for positive solutions of semilinear elliptic boundary value problems},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {19},
     year = {2002},
     pages = {705-714},
     mrnumber = {1922474},
     zbl = {1006.35038},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2002__19_5_705_0}
}

Kawohl, Bernd; Sweers, Guido. Inheritance of symmetry for positive solutions of semilinear elliptic boundary value problems. Annales de l'I.H.P. Analyse non linéaire, Tome 19 (2002) pp. 705-714. http://gdmltest.u-ga.fr/item/AIHPC_2002__19_5_705_0/

[1] Altmann S.L., Herzig P., Point-Group Theory Tables, Clarendon Press, Oxford, 1994.

[2] Berestycki H., Nirenberg L., Monotonicity, symmetry and antisymmetry of solutions of semilinear elliptic equations, J. Geom. Phys. 5 (1988) 237-275. | MR 1029429 | Zbl 0698.35031

[3] Berestycki H., Nirenberg L., On the method of moving planes and the sliding method, Bol. Soc. Brasil. Mat. (N.S.) 22 (1991) 1-37. | MR 1159383 | Zbl 0784.35025

[4] Coffman C.V., A nonlinear boundary value problem with many positive solutions, J. Differential Equations 54 (1984) 429-437. | MR 760381 | Zbl 0569.35033

[5] Coxeter H.S.M., Regular Polytopes, Dover Publications, New York, 1973. | MR 370327 | Zbl 0258.05119 | Zbl 0118.35902

[6] Dancer E.N., The effect of the domain shape on the number of positive solutions of certain nonlinear equations, J. Differential Equations 74 (1988) 120-156. | MR 949628 | Zbl 0662.34025

[7] Dancer E.N., Sweers G., On the existence of a maximal weak solution for a semilinear elliptic equation, Differential Integral Equations 2 (1989) 533-540. | MR 996759 | Zbl 0732.35027

[8] Fraenkel L.E., An Introduction to Maximum Principles and Symmetry in Elliptic Problems, Cambridge Tracts in Mathematics, 128, Cambridge University Press, Cambridge, 2000. | MR 1751289 | Zbl 0947.35002

[9] 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

[10] Kawohl B., A geometric property of level sets of solutions to semilinear elliptic Dirichlet problems, Applicable Anal. 16 (1983) 229-233. | MR 712734 | Zbl 0507.35035

[11] Kawohl B., Symmetry results for functions yielding best constants in Sobolev-type inequalities, Discrete Continuous Dynam. Systems 6 (2000) 683-690. | MR 1757396 | Zbl 01492653

[12] Mcnabb A., A. Strong comparison theorems for elliptic equations of second order, J. Math. Mech. 10 (1961) 431-440. | MR 142881 | Zbl 0106.29903

[13] Mcweeny R., Symmetry, an Introduction to Group Theory and Its Applications, Pergamon Press, Oxford, 1963. | MR 224687 | Zbl 0111.36002

[14] Sweers G., Semilinear elliptic problems on domains with corners, Comm. Partial Differential Equations 14 (1989) 1229-1247. | MR 1017071 | Zbl 0702.35097

[15] Sweers G., Lecture notes on maximum principles, December 2000, http://aw.twi.tudelft.nl/~sweers/maxpr/maxprinc.pdf.