Fine properties of minimizers of mechanical Lagrangians with Sobolev potentials | Zendy

Alessio Figalli | Zendy; Vito Mandorino | Zendy

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Fine properties of minimizers of mechanical Lagrangians with Sobolev potentials

Author(s) -

Alessio Figalli,

Vito Mandorino

Publication year - 2011

Publication title -

discrete and continuous dynamical systems

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.289

H-Index - 70

eISSN - 1553-5231

pISSN - 1078-0947

DOI - 10.3934/dcds.2011.31.1325

Subject(s) - sobolev space , pointwise , compressibility , mathematical analysis , mathematics , point (geometry) , euler equations , potential theory , euler's formula , space (punctuation) , physics , geometry , computer science , mechanics , operating system

22 pagesInternational audienceIn 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

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