Calculus of Variations and Geometric Measure Theory
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A. Clop - R. Giova - F. Hatami - A. Passarelli di Napoli

Congested traffic dynamics and very degenerate elliptic equations under supercritical Sobolev regularity

created by passarell on 22 Mar 2018
modified on 26 Mar 2018


Submitted Paper

Inserted: 22 mar 2018
Last Updated: 26 mar 2018

Year: 2018

ArXiv: 1803.08723 PDF


We study the congested transport dynamics arising from a non-autonomous traffic optimization problem. In this setting, we prove one can find an optimal traffic strategy with support on the trajectories of a DiPerna-Lions flow. The proof follows the scheme introduced by Brasco, Carlier and Santambrogio in the autonomous setting, applied to the case of supercritical Sobolev dependence in the spatial variable. This requires both Lipschitz and weighted Sobolev apriori bounds for the minimizers of a class of integral functionals whose ellipticity bounds are satisfied only away from a ball of the gradient variable.


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