Symmetry for solutions of semilinear elliptic equations in ℝN and related conjectures

Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica E Applicazioni

Volumn 10, Issue 4, 1999, Pages 255-265

  Farina, Alberto ^a  

^a Faculté de Mathématiques et d Informatique   (France)

Author keywords

Maximum principles; Moving planes method; Semilinear elliptic PDE; Symmetry and monotonicity properties

Indexed keywords

EID: 0042398900     PISSN: 11206330     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (18)

1. M. T. BARLOW, On the Liouville property for divergence form operators. Canadian J. Math., 50, 1998, 487-496.
2. M. T. BARLOW - R. F. BASS - C. GUI, The Liouville property and a conjecture of De Giorgi. Preprint.
3. H. BERESTYCKI - L. CAFFARELLI - L. NIRENBERG, Monotonicity for Elliptic Equations in Unbounded Lipschitz Domains. Commun. Pure Appl. Math., 50, 1997, 1089-1111.
4. H. BERESTYCKI - L. CAFFARELLI - L. NIRENBERG, Further Qualitative Properties for Elliptic Equations in Unbounded Domains. Ann. Scuola Norm. Sup. Pisa Cl. Sci., 25 (4), 1997, 69-94.
5. H. BERESTYCKI - F. HAMEL - R. MONNEAU, One-dimensional symmetry for some bounded entire solutions of some elliptic equations. Preprint, 1999.
6. L. CAFFARELLI - N. GAROFALO - F. SEGALA, A Gradient Bound for Entire Solutions of Quasi-Linear Equations and its Consequences. Commun. Pure Appl. Math., 47, 1994, 1457-1473.
7. G. CARBOU, Unicité et minimalité des solutions d'une équation the Ginzburg-Landau. Ann. Inst. H. Poincaré, Analyse non linéaire, 12 (3), 1995, 305-318.
8. E. DE GIORGI, Convergence Problems for Functionals and Operators. In: E. DE GIORGI - E. MAGENES - U. MOSCO (eds.), Proceedings of the Int. Meeting on Recent Methods in Nonlinear Analysis (Rome, 1978). Pitagora, Bologna 1979, 131-188.
9. K. C.R. Acad. Sci. Paris, t. 325, Série I, 1997, 487-491.
10. K. Differential and Integral Equations, vol. 11, 6, 1998, 875-893.
11. A. FARINA, Some remarks on a conjecture of De Giorgi. Calc. Var. Part. Diff. Eq., 8, 1999, 3, 233-245.
12. N and related conjectures. Ricerche di Matematica: special issue in memory of E. De Giorgi, XLVIII, 1999, 129-154.
13. N. GHOUSSOUB - C. GUI, On a conjecture of De Giorgi and some related problems. Math. Annalen, 311, 1998, 481-491.
14. A.N. KOLMOGOROV - I. G. PETROVSKY - N. S. PISKUNOV, Étude de l'équation de la diffusion avec croissance de la quantité de matière et son application à un problème biologique. Bull. Univ. Etat Moscou, Série Int. Sect. A, Math. et Mecan., 1, 1937, 1-25.
15. (English translation: Study of the Diffusion Equation with Growth of the Quantity of Matter and its Application to a Biology Problem. In: R. PELCÉ (ed.), Dynamics of curved fronts. Perspectives in Physics Series, Academic Press, New York 1988, 105-130).
16. N. Comm. Part. Diff. Eq., 18, 1993, 1043-1054.
17. L. MODICA, A Gradient Bound and a Liouville Theorem for Nonlinear Poisson Equations. Commun. Pure Appl. Math., 38, 1985, 679-684.
18. L. MODICA - S. MORTOLA, Some Entire Solutions in the Plane of Nonlinear Poisson Equations. Boll. Un. Mat. Ital., 17-B, 1980, 614-622.