Fine properties of minimizers of mechanical Lagrangians with Sobolev potentials
Mandorino, Vito; Figalli, Alessio (2011), Fine properties of minimizers of mechanical Lagrangians with Sobolev potentials, Discrete and Continuous Dynamical Systems. Series A, 31, 4, p. 1325-1346. http://dx.doi.org/10.3934/dcds.2011.31.1325
TypeArticle accepté pour publication ou publié
External document linkhttp://hal.archives-ouvertes.fr/hal-00636941/fr/
Journal nameDiscrete and Continuous Dynamical Systems. Series A
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Abstract (EN)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.
Subjects / Keywordsvalue function; action-minimizing measures; Euler-Lagrange equations; Non-smooth Lagrangians
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