On a class of optimal partition problems related to the Fučík spectrum and to the monotonicity formulae

Calculus of Variations and Partial Differential Equations

Volumn 22, Issue 1, 2005, Pages 45-72

  Conti, Monica ^a   Terracini, Susanna ^b   Verzini, Gianmaria ^a  

^a POLITECNICO DI MILANO   (Italy)

^b UNIVERSITY OF MILANO BICOCCA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 12144264150     PISSN: 09442669     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00526-004-0266-9     Document Type: Article

References (23)

1. Alt, H.W., Caffarelli, L.A., Friedman, A.: Variational problems with two phases and their free boundaries. Trans. A.M.S. 282, 431-461 (1984)
2. Brown, B.M., Reichel, W.: Computing eigenvalues and Fučík- spctrum of the radial p-Laplacian. J. Comput. Appl. Math. 148, 183-211 (2002)
3. n. Preprint 2002
4. Bucur, D., Buttazzo, G., Henrot, A.: Existence results for some optimal partition problems. Adv. Math. Sci. Appl. 8, 571-579 (1998)
5. Buttazzo, G., Timofte, C.: On the relaxation of some optimal partition problems. Adv. Math. Sci. Appl. 12 (2), 509-520 (2002)
6. Caffarelli, L.A., Karp, L., Shahgholian, H.: Regularity of a free boundary with applications to the Pompeiu problem. Annals Math. 151, 269-292 (2000)
7. Conti, M., Terracini, S., Verzini, G.: An optimal partition problem related to nonlinear eigenvalues. J. Funct. Anal. 198, 160-196 (2003)
8. Conti, M., Terracini, S., Verzini, G.: A variational problem for the spatial segregation of reaction-diffusion systems. Preprint (2003)
9. Conti, M., Terracini, S., Verzini, G.: Asymptotic estimates for the spatial segregation of competitive systems. Preprint (2004)
10. Cuesta, M., De Figuereido, D.G., Gossez, J.-P: The beginning of the Fučík spectrum for the p-laplacian. J. Differential Equations 159, 212-238 (1999)
11. Dancer, E.N.: On the Dirichlet problem for weakly nonlinear elliptic partial differential equations. Proc. Roy. Soc. Edinburgh Sect. A 76, 283-300 (1977)
12. Dancer, E.N.: Competing species systems with diffusion and large interaction. Rend. Sem. Mat. Fis. Milano 65, 23-33 (1995)
13. Dancer, E.N., Du, Y.H.: Competing species equations with diffusion, large interactions, and jumping nonlinearities. J. Differential Equations 114, 434-475 (1994)
14. Dancer, E.N., Guo, Z.M.; Uniqueness and stability for solutions of competing species equations with large interactions. Comm. Appl. Nonlinear Anal. 1, 19-45 (1994)
15. Dancer, E.N., Hilhorst, D., Mimura, M., Peletier, L.A.: Spatial segregation limit of a competition-diffusion system. European J. Appl. Math. 10, 97-115 (1999)
16. De Figuereido, D.G., Gossez, J.-P.: On the first curve of the Fučík spectrum of an elliptic operator. Differential Integral Equations 7, 1285-1302 (1994)
17. De Figuereido, D.G., Ruf, B.: On the periodic Fučík spectrum and a superlinear Sturm-Liouville equation. Proc. Roy. Soc. Edinburgh Sect A 123, 95-107 (1993)
18. Fučík, S.: Solvability of nonlinear equations and boundary value problems. (Mathematics and its applications, Vol. 4) Reidel, Dordrect/Boston 1980
19. Horák, J., Reichel, W.: Analytical and numerical results for the Fučík spectrum of the Laplacian. Preprint (2002). J. Comp. Appl. Math (to appear)
20. Korman, P., Leung, A.: On the existence and uniqueness of positive steady states in Lotka-Volterra ecological models with diffusion. Appl. Anal. 26, 145-160 (1987)
21. Lazer, A.C., McKenna, P.J.: On steady state solutions of a system of reaction-diffusion equations from biology. Nonlinear Anal. TMA 6, 523-530 (1982)
22. Miranda, C.: Un'osservazione sul teorema di Brouwer. Boll. U.M.I. Serie II, Anno II, 1, 5-7 (1940)
23. Sperner, E.: Zur Symmetrisierung von Funktionen auf Sphären. Math. Z. 134, 317-330 (1973)