Symmetry of large solutions of nonlinear elliptic equations in a ball

Journal of Functional Analysis

Volumn 236, Issue 2, 2006, Pages 581-591

  Porretta, Alessio ^a   Véron, Laurent ^b  

^a UNIVERSITY OF ROME TOR VERGATA   (Italy)

^b UNIVERSITÉ DE TOURS   (France)

Author keywords

Boundary blow up; Elliptic equations; Keller Osserman condition; Radial symmetry; Spherical Laplacian

Indexed keywords

EID: 33646356694     PISSN: 00221236     EISSN: 10960783     Source Type: Journal    
DOI: 10.1016/j.jfa.2006.03.010     Document Type: Article

References (18)

1. Aftalion A., del Pino M., and Letelier R. Multiple boundary blow-up solutions for nonlinear elliptic equations. Proc. Roy. Soc. Edinburgh Sect. A 133 2 (2003) 225-235
2. Bandle C., and Essen M. On the solutions of quasilinear elliptic problems with boundary blow-up. Sympos. Math. vol. 35 (1994), Cambridge Univ. Press 93-111
3. Bandle C., and Marcus M. Large solutions of semilinear elliptic equations: Existence, uniqueness and asymptotic behaviour. J. Anal. Math. 58 (1992) 9-24
4. Bandle C., and Marcus M. Asymptotic behaviour of solutions and their derivatives, for semilinear elliptic problems with blowup on the boundary. Ann. Inst. H. Poincaré Anal. Non Linéaire 12 2 (1995) 155-171
5. H. Brezis, personal communication, January 2005
6. Du Y., and Guo Z. Boundary blow-up solutions and their applications in quasilinear elliptic equations. J. Anal. Math. 89 (2003) 277-302
7. Du Y., and Guo Z. Uniqueness and layer analysis for boundary blow-up solutions. J. Math. Pures Appl. 83 6 (2004) 739-763
8. Du Y., and Yan S. Boundary blow-up solutions with a spike layer. J. Differential Equations 205 1 (2004) 156-184
9. Gidas B., Ni W.M., and Nirenberg L. Symmetry and related properties via the maximum principle. Comm. Math. Phys. 68 (1979) 209-243
10. Keller J.B. On solutions of Δ u = f ( u ). Comm. Pure Appl. Math. 10 (1957) 503-510
11. Marcus M., and Véron L. Uniqueness and asymptotic behaviour of solutions with boundary blow-up for a class of nonlinear elliptic equations. Ann. Inst. H. Poincaré 14 (1997) 237-274
12. Marcus M., and Véron L. Existence and uniqueness results for large solutions of general nonlinear elliptic equations. J. Evol. Equ. 3 (2003) 637-652
13. McKenna P.J., Reichel W., and Walter W. Symmetry and multiplicity for nonlinear elliptic differential equations with boundary blow-up. Nonlinear Anal. 28 7 (1997) 1213-1225
14. Osserman R. On the inequality Δ u {greater than or slanted equal to} f ( u ). Pacific J. Math. 7 (1957) 1641-1647
15. 2. Dokl. Akad. Nauk SSSR 138 (1961) 305-308 (in Russian)
16. A. Porretta, L. Véron, Asymptotic behaviour for the gradient of large solutions to some nonlinear elliptic equations, Adv. Nonlinear Stud., in press
17. Serrin J. A symmetry problem in potential theory. Arch. Rat. Mech. Anal. 43 (1971) 304-318
18. Véron L. Semilinear elliptic equations with uniform blow-up on the boundary. J. Anal. Math. 59 (1992) 231-250