Vol. 9, No. 5, 2016

Download this article
Download this article For screen
For printing
Recent Issues

Volume 10
Issue 7, 1539–1791
Issue 6, 1285–1538
Issue 5, 1017–1284
Issue 4, 757–1015
Issue 3, 513–756
Issue 2, 253–512
Issue 1, 1–252

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
Cover
About the Cover
Editorial Board
Editors’ Interests
About the Journal
Scientific Advantages
Submission Guidelines
Submission Form
Subscriptions
Editorial Login
Contacts
Author Index
To Appear
 
ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
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

ΔV i = V i jiV j2,V i > 0  in N,

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 N 3. 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