# American Institute of Mathematical Sciences

December  2011, 31(4): 1325-1346. doi: 10.3934/dcds.2011.31.1325

## Fine properties of minimizers of mechanical Lagrangians with Sobolev potentials

 1 University of Texas at Austin, Department of Mathematics, 2515 Speedway Stop C1200, Austin, TX 78712-1202, United States 2 Université Paris-Dauphine, CEREMADE UMR CNRS 7534, Place du Maréchal de Lattre de Tassigny, 75775 Paris Cedex 16, France

Received  November 2009 Revised  August 2010 Published  September 2011

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.
Citation: Alessio Figalli, Vito Mandorino. Fine properties of minimizers of mechanical Lagrangians with Sobolev potentials. Discrete & Continuous Dynamical Systems - A, 2011, 31 (4) : 1325-1346. doi: 10.3934/dcds.2011.31.1325
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