Calculus of Variations and Geometric Measure Theory
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G. Fusco - G. F. Gronchi - M. Novaga

On the existence of heteroclinic connections

created by novaga on 24 Feb 2017


Submitted Paper

Inserted: 24 feb 2017
Last Updated: 24 feb 2017

Year: 2017


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 $a_+\in A \setminus \{a_- \}$.


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