On a class of optimal partition problems related to the Fuč\'ık spectrum and to the monotonicity formulae
| dc.creator | Conti, Monica | |
| dc.creator | Terracini, Susanna | |
| dc.creator | Verzini, Gianmaria | |
| dc.date | 2003-12-10 | |
| dc.date.accessioned | 2026-07-07T05:03:45Z | |
| dc.date.available | 2026-07-07T05:03:45Z | |
| dc.description | In this paper we give an unified approach to some questions arising in different fields of nonlinear analysis, namely: (a) the study of the structure of the Fuč\'ık spectrum and (b) possible variants and extensions of the monotonicity formula by Alt--Caffarelli--Friedman \cite{acf}. In the first part of the paper we present a class of optimal partition problems involving the first eigenvalue of the Laplace operator. Beside establishing the existence of the optimal partition, we develop a theory for the extremality conditions and the regularity of minimizers. As a first application of this approach, we give a new variational characterization of the first curve of the Fuč\'ık spectrum for the Laplacian, promptly adapted to more general operators. In the second part we prove a monotonicity formula in the case of many subharmonic components and we give an extension to solutions of a class of reaction--diffusion equation, providing some Liouville--type theorems. | |
| dc.description | 21 pages | |
| dc.identifier | https://arxiv.org/abs/math/0312207 | |
| dc.identifier | http://arxiv.org/abs/math/0312207 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69544 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Functional Analysis | |
| dc.subject | 35J65; 58E05 | |
| dc.title | On a class of optimal partition problems related to the Fuč\'ık spectrum and to the monotonicity formulae | |
| dc.type | text |