# American Institute of Mathematical Sciences

August  2006, 15(3): 833-842. doi: 10.3934/dcds.2006.15.833

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

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

Received  June 2005 Revised  November 2005 Published  April 2006

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.
Citation: Flavia Antonacci, Marco Degiovanni. On the Euler equation for minimal geodesics on Riemannian manifoldshaving discontinuous metrics. Discrete and Continuous Dynamical Systems, 2006, 15 (3) : 833-842. doi: 10.3934/dcds.2006.15.833
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