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.
Antonacci, F., Degiovanni, M., On the Euler equation for minimal geodesics on Riemannian manifolds having discontinuous metrics, <<DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS>>, 2006; 15 (3): 833-842 [http://hdl.handle.net/10807/5133]
On the Euler equation for minimal geodesics on Riemannian manifolds having discontinuous metrics
Degiovanni, Marco
2006
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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