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Discrete and Continuous Dynamical Systems - Series A 31, 4 (2011) 1325 -- 1346
Fine properties of minimizers of mechanical Lagrangians with Sobolev potentials
Alessio Figalli1, Vito Mandorino2

In this paper we study the properties of curves minimizing mechanical Lagrangian where the potential is Sobolev. Since a Sobolev function is only defined almost everywhere, no pointwise results can be obtained in this framework, and our point of view is shifted from single curves to measures in the space of paths. This study is motived by the goal of understanding the properties of variational solutions to the incompressible Euler equations.
1 :  Department of Mathematics and Statistics [Texas Tech]
2 :  CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
Non-smooth Lagrangians – Euler-Lagrange equations – action-minimizing measures – value function.