DCDS
On the Euler equation for minimal geodesics on Riemannian manifoldshaving discontinuous metrics
Flavia Antonacci Marco Degiovanni
Discrete & Continuous Dynamical Systems - A 2006, 15(3): 833-842 doi: 10.3934/dcds.2006.15.833
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.
keywords: minimal geodesics. refraction problems Riemannian manifolds discontinuous metrics
DCDS
A variational approach to semilinear elliptic equations with measure data
Marco Degiovanni Michele Scaglia
Discrete & Continuous Dynamical Systems - A 2011, 31(4): 1233-1248 doi: 10.3934/dcds.2011.31.1233
We describe a direct variational approach to a class of semilinear elliptic equations with measure data. Using a typical variational argument, we show the existence of multiple solutions.
keywords: measure data. semilinear elliptic equations Variational methods

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