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SUMMARY:A generalized Dacorogna-Moser construction and the  problem of geo
 desics in the space of couplings
DTSTART:20260624T083000Z
DTEND:20260624T100000Z
DTSTAMP:20260706T081800Z
UID:indico-event-16878@indico.math.cnrs.fr
DESCRIPTION:Speakers: Matteo Picco (EPFL)\n\n\n\n\nThe seminal work by Dac
 orogna and Moser introduced a way to\nconstruct transport maps with high r
 egularity from a probability\ndistribution to another on a bounded domain.
  In this work\, we\ngeneralize the Dacorogna-Moser construction to strictl
 y\nasymptotically log-concave measures on non-compact domains\, by\nestabl
 ishing uniform-in-time estimates on parabolic and elliptic\nPDEs defined o
 n the whole space. Then\, we study the application\nof this result to the 
 analysis of the problem of geodesics in the\nspace of couplings with two g
 iven marginals\, solving an open\nquestion in Conforti\, Lacker\, Pal [JEM
 S'25]. In particular we study\nthe existence of minimizers\, the existence
  of a Lagrange multiplier\n\n\n\n\n\n\n\nassociated to the marginal constr
 aints and the optimality conditions\;\nfurthermore\, we introduce a suitab
 le regularization and we prove Γ-\nconvergence to the original problem an
 d weak-* convergence of the\nLagrange multipliers in a proper space\, simi
 larly to what is done in\nBaradat\, Monsaingeon [ARMA'20]\n\n\n\n\n \n\nh
 ttps://indico.math.cnrs.fr/event/16878/
LOCATION:112 (Braconnier)
URL:https://indico.math.cnrs.fr/event/16878/
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