Calculus of Variations and Geometric Measure Theory
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H. Lavenant - F. Santambrogio

Optimal density evolution with congestion: $L^\infty$ bounds via flow interchange techniques and applications to variational Mean Field Games

created by santambro on 31 Mar 2017



Inserted: 31 mar 2017
Last Updated: 31 mar 2017

Year: 2017

paper still to be submitted, any comment is welcome


We consider minimization problems for curves of measure, with kinetic and potential energy and a congestion penalization, as in the functionals that appear in Mean Field Games with a variational structures. We prove $L^\infty$ regularity results for the optimal density via time-discretization arguments, displacement convexity, and suitable Moser iterations.


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