|
|||||
 |
|
|
|
|
Multidimensional entire
solutions for an elliptic system modelling phase
separation
Nicola Soave and Alessandro Zilio |
|
Vol. 9 (2016), No. 5, 1019–1041
|
Abstract |
|
For the system of semilinear elliptic equations we devise a new method to construct entire solutions. The method extends the existence results already available in the literature, which are concerned with the 2-dimensional case, also to higher dimensions . In particular, we provide an explicit relation between orthogonal symmetry subgroups, optimal partition problems of the sphere, the existence of solutions and their asymptotic growth. This is achieved by means of new asymptotic estimates for competing systems and new sharp versions for monotonicity formulae of Alt–Caffarelli–Friedman type. |
Keywords
entire solutions of elliptic systems, Liouville theorem,
nonlinear Schrödinger systems, Almgren monotonicity
formula, optimal partition problems, equivariant solutions
|
Mathematical Subject Classification 2010
Primary: 35B06, 35B08, 35B53
Secondary: 35B40, 35J47
|
Milestones
Received: 16 July 2015
Revised: 5 February 2016
Accepted: 29 April 2016
Published: 29 July 2016
|
Authors |
| Nicola Soave | |
| Mathematisches Institut Justus-Liebig-Universität Giessen Arndtstrasse 2 35392 Giessen Germany |
|
| Alessandro Zilio | |
| Centre d’Analyse et de Mathématique
Sociales École des Hautes Études en Sciences Sociales 190–198 Avenue de France 75244 Paris CEDEX 13 France |
|
|
