Monotonicity and symmetry of solutions of -Laplace equations, , via the moving plane method
Lucio Damascelli; Filomena Pacella
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1998)
- Volume: 26, Issue: 4, page 689-707
- ISSN: 0391-173X
Access Full Article
topHow to cite
topReferences
top- [BN] H. Berestycki - L. Nirenberg, On the method of moving planes and the sliding method, Bol. Soc. Brasil. Mat.22 (1991), 1-37. Zbl0784.35025MR1159383
- [BaNa] M. Badiale - E. Nabana, A note on radiality of solutions of p-Laplacian equations, Appl. Anal.52 (1994), 35-43. Zbl0841.35008MR1380325
- [Br] F. Brock, Continuous Rearrangement and symmetry of solutions of elliptic problems, Habilitation thesis, Cologne (1997).
- [D] E.N. Dancer, Some notes on the method of moving planes, Bull. Austral. Math. Soc.46 (1992), 425-434. Zbl0777.35005MR1190345
- [Da1] L. Damascelli, Some remarks on the method of moving planes, Differential Integral Equations, 11, 3 (1998), 493-501. Zbl1040.35032MR1745551
- [Da2] L. Damascelli, Comparison theorems for some quasilinear degenerate elliptic operators and applications to symmetry and monotonicity results, Ann. Inst. H. Poincaré Anal. Non Linéaire, to appear. Zbl0911.35009MR1632933
- [Di] E. Dibenedetto, C1+α local regularity of weak solutions of degenerate elliptic equations, Nonlinear Anal.7 (8) (1993), 827-850. Zbl0539.35027
- [GNN] B. Gidas - W.M. Ni - L. Nirenberg, Symmetry and related properties via the maximum principle, Comm. Math. Phys.68 (1979), 209-243. Zbl0425.35020MR544879
- [GKPR] M. Grossi - S. Kesavan - F. Pacella - M. Ramaswami, Symmetry of positive solutions of some nonlinear equations, Topol. Methods Nonlinear Analysis, to appear. Zbl0927.35039MR1677751
- [H] H. Hopf, "Lectures on differential geometry in the large", Stanford University, 1956. Zbl0669.53001
- [KP] S. Kesavan - F. Pacella, Symmetry of positive solutions of a quasilinear elliptic equation via isoperimetric inequality, Appl. Anal.54 (1994), 27-37. Zbl0833.35040MR1382205
- [N] A. Norton, A critical set with nonnull image has a large Hausdorff dimension, Trans. Amer. Math. Soc.296 (1986), 367-376. Zbl0596.26008MR837817
- [S] J. Serrin, A symmetry problem in potential theory, Arch. Rational Mech. Anal.43 (1971), 304-318. Zbl0222.31007MR333220
- [T] P. Tolksdorf, Regularity for a more general class of quasilinear elliptic equations, J. Diff. Equations51 (1984), 126-150. Zbl0488.35017MR727034
- [V] J.L. Vazquez, A strong maximum principle for some quasilinear elliptic equations, Appl. Math. Optim. (1984), 191-202. Zbl0561.35003MR768629
- [W] H. Whitney, A function not constant on a connected set of critical points, Duke Math. J.1 (1935), 514-517. Zbl0013.05801MR1545896JFM61.1117.01