Analysis & PDE
- Anal. PDE
- Volume 9, Number 5 (2016), 1019-1041.
Multidimensional entire solutions for an elliptic system modelling phase separation
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.
Anal. PDE, Volume 9, Number 5 (2016), 1019-1041.
Received: 16 July 2015
Revised: 5 February 2016
Accepted: 29 April 2016
First available in Project Euclid: 12 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 35B06: Symmetries, invariants, etc. 35B08: Entire solutions 35B53: Liouville theorems, Phragmén-Lindelöf theorems
Secondary: 35B40: Asymptotic behavior of solutions 35J47: Second-order elliptic systems
Soave, Nicola; Zilio, Alessandro. Multidimensional entire solutions for an elliptic system modelling phase separation. Anal. PDE 9 (2016), no. 5, 1019--1041. doi:10.2140/apde.2016.9.1019. https://projecteuclid.org/euclid.apde/1513097063