Mather theory for lower semicontinuous Lagrangians

Giovedi' 19 Luglio 2012 - Gabriele Terrone


Giovedi' 19 Luglio 2012 alle ore 14:15 in aula 1BC45, Gabriele Terrone (Instituto Superior Tecnico de Lisboa) terra' un seminario dal titolo "Mather theory for lower semicontinuous Lagrangians".

The Mather problem consists in finding a measure minimizing the integral of a given Lagrangian L(x,v) in a suitable class of probability measures. I will present some results, obtained in collaboration with Diogo Gomes (Instituto Superior Tecnico de Lisboa), in which we develop the Mather theory for Lagrangians that are discontinuous. Precisely we consider Lagrangians that are merely lower semicontinuous in the state variable x, but convex and coercive in the velocity variable v. I will start with a brief review of the theory in the continuous case, originated with the pioneering work by John Mather (1991) and Ricardo Mane' (1996). Then, after a discussion about necessary conditions that must be satisfied by trajectories that minimize the action functional with a discontinuous Lagrangian, I will discuss the existence of holonomic minimizing probability measures and some properties related with the invariance of such minimizers with respect to the Euler-Lagrange flow.

Rif. int. M. Bardi, P. Mannucci, C. Marchi

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