We extend to the case of many competing densities the results of the paper (Ann. Inst. H. Poincare 6 (2002)). More precisely, we are concerned with an optimal partition problem in N-dimensional domains related to the method of nonlinear eigenvalues introduced by Nehari, (Acta Math. 105 (1961)). We prove existence of the minimal partition and some extremality conditions. Moreover, in the case of two-dimensional domains we give an asymptotic formula near the multiple intersection points. Finally, we show some connections between the variational problem and the behavior of competing species systems with large interaction. (C) 2002 Elsevier Science (USA)
Conti, M., Terracini, S., Verzini, G. (2003). An optimal partition problem related to nonlinear eigenvalues. JOURNAL OF FUNCTIONAL ANALYSIS, 198(1), 160-196 [10.1016/S0022-1236(02)00105-2].
An optimal partition problem related to nonlinear eigenvalues
TERRACINI, SUSANNA;
2003
Abstract
We extend to the case of many competing densities the results of the paper (Ann. Inst. H. Poincare 6 (2002)). More precisely, we are concerned with an optimal partition problem in N-dimensional domains related to the method of nonlinear eigenvalues introduced by Nehari, (Acta Math. 105 (1961)). We prove existence of the minimal partition and some extremality conditions. Moreover, in the case of two-dimensional domains we give an asymptotic formula near the multiple intersection points. Finally, we show some connections between the variational problem and the behavior of competing species systems with large interaction. (C) 2002 Elsevier Science (USA)
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