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2015 A topological join construction and the Toda system on compact surfaces of arbitrary genus
Aleks Jevnikar, Sadok Kallel, Andrea Malchiodi
Anal. PDE 8(8): 1963-2027 (2015). DOI: 10.2140/apde.2015.8.1963

Abstract

We consider the Toda system of Liouville equations on a compact surface Σ

Δu1 = 2ρ1( h1eu1 Σh1eu1dV g 1) ρ2( h2eu2 Σh2eu2dV g 1), Δu2 = 2ρ2( h2eu2 Σh2eu2dV g 1) ρ1( h1eu1 Σh1eu1dV g 1),

which arises as a model for nonabelian Chern–Simons vortices. Here h1 and h2 are smooth positive functions and ρ1 and ρ2 two positive parameters.

For the first time, the ranges ρ1 (4kπ,4(k + 1)π), k , and ρ2 (4π,8π) are studied with a variational approach on surfaces with arbitrary genus. We provide a general existence result by using a new improved Moser–Trudinger-type inequality and introducing a topological join construction in order to describe the interaction of the two components u1 and u2.

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Aleks Jevnikar. Sadok Kallel. Andrea Malchiodi. "A topological join construction and the Toda system on compact surfaces of arbitrary genus." Anal. PDE 8 (8) 1963 - 2027, 2015. https://doi.org/10.2140/apde.2015.8.1963

Information

Received: 19 March 2015; Accepted: 7 September 2015; Published: 2015
First available in Project Euclid: 16 November 2017

zbMATH: 1336.35152
MathSciNet: MR3441211
Digital Object Identifier: 10.2140/apde.2015.8.1963

Subjects:
Primary: 35J50, 35J61, 35R01

Rights: Copyright © 2015 Mathematical Sciences Publishers

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