@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] Point-Group Theory Tables, Clarendon Press, Oxford, 1994.
, ,[2] Monotonicity, symmetry and antisymmetry of solutions of semilinear elliptic equations, J. Geom. Phys. 5 (1988) 237-275. | MR 1029429 | Zbl 0698.35031
, ,[3] 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] A nonlinear boundary value problem with many positive solutions, J. Differential Equations 54 (1984) 429-437. | MR 760381 | Zbl 0569.35033
,[5] Regular Polytopes, Dover Publications, New York, 1973. | MR 370327 | Zbl 0258.05119 | Zbl 0118.35902
,[6] 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] 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] 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] Symmetry and related properties via the maximum principle, Comm. Math. Phys. 68 (1979) 209-243. | MR 544879 | Zbl 0425.35020
, , ,[10] 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] Symmetry results for functions yielding best constants in Sobolev-type inequalities, Discrete Continuous Dynam. Systems 6 (2000) 683-690. | MR 1757396 | Zbl 01492653
,[12] A. Strong comparison theorems for elliptic equations of second order, J. Math. Mech. 10 (1961) 431-440. | MR 142881 | Zbl 0106.29903
,[13] Symmetry, an Introduction to Group Theory and Its Applications, Pergamon Press, Oxford, 1963. | MR 224687 | Zbl 0111.36002
,[14] Semilinear elliptic problems on domains with corners, Comm. Partial Differential Equations 14 (1989) 1229-1247. | MR 1017071 | Zbl 0702.35097
,[15] Lecture notes on maximum principles, December 2000, http://aw.twi.tudelft.nl/~sweers/maxpr/maxprinc.pdf.
,