Calculus of Variations and Geometric Measure Theory

G. Fusco - G. F. Gronchi - M. Novaga

On the existence of heteroclinic connections

created by novaga on 24 Feb 2017
modified on 30 Apr 2018


Published Paper

Inserted: 24 feb 2017
Last Updated: 30 apr 2018

Journal: São Paulo Journal of Mathematical Sciences
Volume: 12
Number: 1
Pages: 68-81
Year: 2018


Assume that $W : \mathbb R^m \to \mathbb R$ is a nonnegative potential that vanishes only on a finite set $A$ with at least two elements. By direct minimization of the action functional on a suitable set of maps we give a new elementary proof of the existence of a heteroclinic orbit that connects any given $a_-\in A$ to some $a_+\in A \setminus \{a_- \}$.