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2016 Multidimensional entire solutions for an elliptic system modelling phase separation
Nicola Soave, Alessandro Zilio
Anal. PDE 9(5): 1019-1041 (2016). DOI: 10.2140/apde.2016.9.1019

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.

Citation

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Nicola Soave. Alessandro Zilio. "Multidimensional entire solutions for an elliptic system modelling phase separation." Anal. PDE 9 (5) 1019 - 1041, 2016. https://doi.org/10.2140/apde.2016.9.1019

Information

Received: 16 July 2015; Revised: 5 February 2016; Accepted: 29 April 2016; Published: 2016
First available in Project Euclid: 12 December 2017

zbMATH: 1342.35022
MathSciNet: MR3531365
Digital Object Identifier: 10.2140/apde.2016.9.1019

Subjects:
Primary: 35B06, 35B08, 35B53
Secondary: 35B40, 35J47

Rights: Copyright © 2016 Mathematical Sciences Publishers

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