On the Euler equation for minimal geodesics on Riemannian manifoldshaving discontinuous metrics

Flavia Antonacci; Marco Degiovanni

doi:10.3934/dcds.2006.15.833

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2006, Volume 15, Issue 3: 833-842. Doi: 10.3934/dcds.2006.15.833

This issue Previous Article Global stability of traveling curved fronts in the Allen-Cahn equations Next Article On stochastic stabilization of difference equations

On the Euler equation for minimal geodesics on Riemannian manifoldshaving discontinuous metrics

Flavia Antonacci^1, and
Marco Degiovanni^2,

1.
Dipartimento di Scienze, Università di Pescara, Viale Pindaro 82, 65127 Pescara
2.
Dipartimento di Matematica e Fisica, Università Cattolica del Sacro Cuore, Via dei Musei 41, 25121 Brescia

Received: May 31, 2005

Revised: October 31, 2005

Published: August 2006

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Abstract

We provide a qualitative description of curves minimizing the energy functional on a Riemannian manifold whose metric is discontinuous along a hypersurface $\Sigma$. Such a study is motivated by the variational description of refraction phenomena.

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Mathematics Subject Classification: Primary: 58E10; Secondary: 53C22.

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