Some new symmetry results for elliptic problems on the sphere and in Euclidean space

Rendiconti del Circolo Matematico di Palermo

Volumn 49, Issue 3, 2000, Pages 445-462

  Brock, F ^a   Prajapat, J ^b  

^a UNIVERSITY OF LEIPZIG   (Germany)

^b TATA INSTITUTE OF FUNDAMENTAL RESEARCH   (India)

Author keywords

elliptic equation; maximum principle; rearrangement; stereographic projection; symmetry of the solution

Indexed keywords

EID: 21644488211     PISSN: 0009725X     EISSN: 19734409     Source Type: Journal    
DOI: 10.1007/BF02904257     Document Type: Article

References (27)

1. Allegretto W., Siegel D., Picone's identity and the moving plane procedure, Electronic Journ. Different. Equations, 14 (1995), 1-13.
2. Bandle C., Brillard A., Flucher M., Green's function, harmonic transplantation, and best Sobolev constant in spaces of constant curvature, Transactions of A. M. S., 350 (1998), 1103-1128.
3. 3, preprint, 1998.
4. Berenstein C., Karlovitz M., Some examples to solutions of overdetermined boundary value problems on domains on spheres, preprint, 1991.
5. Berestycki H., Nirenberg L., On the method of moving planes and the sliding method, Bol. Soc. Bras. Mat., 22 (1991), 1-37.
6. Brock F., Continuous Steiner-symmetrization, Math. Nachrichten, 172 (1995), 25-48.
7. Brock F., Continuous rearrangement and symmetry of solutions of elliptic problems, to appear in: Proc. Indian. Math. Soc.
8. Brock F., Radial symmetry for nonnegative solutions of semilinear elliptic problems involving the p-Laplacian, in: Progress in partial differential equations. Pontá-Mousson 1997, Vol. 1, eds. H. Amann et al, 46-58.
9. Brock F., Solynin Yu A., An approach to symmetrization via polarization, to appear in: Transactions of A. M. S.
10. Colesanti A., A symmetry result for p-Laplacian equation via the moving planes method, Applicable Analysis, 55 (1994), 207-213.
11. Dancer E. N., Some notes on the method of moving planes, Bull. Austr. Math. Soc., 46 (1992), 425-434.
12. Damascelli L., Comparison theorems for some quasilinear degenerate elliptic operators and applications to symmetry and monotonicity results, to appear in: Annales Inst. H. Poincare.
13. Damascelli L., Pacella F., Monotonicity and symmetryof solutions of p-Laplace equations, 1< p< 2, via the moving plane method, to appeare in: Ann. Scuola Norm. Sup. Pisa.
14. Diaz J. I., Saa J. E., Existence et unicité de solutions positieves pour certaines équations elliptiques quasilinéaires, Comptes Rendus Acad. Sc. Paris305, Série I (1987), 521-524.
15. Fleckinger J., Hernandez J., de Thelin F., On maximum principles and the existence of positive solutions for some cooperative elliptic systems, 8 (1995), 69-85.
16. Garofalo N., Lewis J. L., A symmetry result related to some overdetermined boundary value problems, American J. Math., 111 (1989), 9-33.
17. Gidas B., Ni W. M., Nirenberg L., Symmetry and relate properties via the maximum principle, Comm. Math. Phys., 68 (1979), 209-243.
18. Guedda M., Veron L., Quasilinear elliptic equations involving citical Sobolev exponents, Nonlinear Anal., T. M. A., 13 (1989), 879-902.
19. Guo Z., Existence and uniqueness of positive radial solutions for a class of quasilinear elliptic equations, Applicable Analysis, 47 (1992), 173-189.
20. Kawohl B., Symmetry, or not?, Math. Intelligencer, 20 (1998), 16-22.
21. Kesavan S., Pacella F., Symmetry of positive solutions of a quasilinear elliptic equation via isoperimetric inequalities, Applicable Analysis - bf54 (1994), 7-17.
22. Kumaresan S., Prajapat J., Serrin's result for hyperbolic space and sphere, Duke Math. Jr., 91 (1998), 17-28.
23. Molzon R., Symmetry and overdetermined boundary value problems, Forum Math., 3 (1991), 143-156.
24. Padilla P., Symmetry properties of positive solutions of elliptic equations on symmetric domains, Journ. Appl. Anal., 64 (1997), 153-169.
25. Serrin J., A symmetry theorem in potential theory, Arch. Rational Mech. Anal., 43 (1971), 126-150.
26. Vazquez J. L., A strong maximum principle for some quasilinear elliptic equations, Appl. Math. Optim., 12 (1984), 191-202.
27. Vogel A. L., Symmetry and regularity for general regions having a solution to certain overdetermined boundary value problems, Atti Sem. Mat. Fis. Univ. Modena, 40 (1992), 443-484.