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DTSTART:20070311T020000
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DTSTAMP:20231208T074623
DTSTART;TZID=America/Detroit:20231220T140000
DTEND;TZID=America/Detroit:20231220T150000
SUMMARY:Workshop / Seminar:Free boundary regularity and support propagation in mean field games and optimal transport
DESCRIPTION:This talk presents recent findings on the regularity of first-order mean\nfield game systems with a local coupling. We focus on systems where the initial\ndensity is a compactly supported function on the real line. Our results show that\nthe solution is smooth in regions where the density is strictly positive and that\nthe density itself is globally continuous. Additionally\, the speed of propagation\nis determined by the behavior of the cost function for small densities. When the\ncoupling is entropic\, we demonstrate that the support of the density propagates\nwith infinite speed. On the other hand\, when f(m) = mθ with θ > 0\, we prove\nthat the speed of propagation is finite. In this case\, we establish that under\na natural non-degeneracy assumption\, the free boundary is strictly convex and\nenjoys C1\,1\nregularity. We also establish sharp estimates on the speed of support\npropagation and the rate of long-time decay for the density. Our methods are based on analyzing a new elliptic equation satisfied by the flow of optimal trajectories. The results also apply to mean field planning problems\, characterizing the structure of minimizers of a class of optimal transport problems with congestion.
UID:115940-21835868@events.umich.edu
URL:https://events.umich.edu/event/115940
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics
LOCATION:Off Campus Location
CONTACT:
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