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Universität Augsburg
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Universität Augsburg
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Professor Dr. Tobias Ried
(MPI Leipzig)
spricht am
Donnerstag, 24. November 2022
um
15:45 Uhr
im
TUM, Boltzmann-3, Garching, Raum 03.08.011, Etage 3
über das Thema:
| Abstract: |
| In this talk I want to present a purely variational approach to the regularity theory for the Monge-Ampère equation, or rather optimal transportation, introduced by Goldman—Otto. Following De Giorgi’s strategy for the regularity theory of minimal surfaces, it is based on the approximation of the displacement by a harmonic gradient, which leads to a one-step improvement lemma, and feeds into a Campanato iteration on the C^{1,\alpha}-level for the displacement. The variational approach is flexible enough to cover general cost functions by importing the concept of almost-minimality: if the cost is quantitatively close to the Euclidean cost function |x-y|^2, a minimiser for the optimal transport problem with general cost is an almost-minimiser for the one with quadratic cost. This allows us to reprove the C^{1,\alpha}-regularity result of De Philippis—Figalli, while bypassing Caffarelli’s celebrated theory. (This is joint work with F. Otto and M. Prod’homme) |
| Hierzu ergeht herzliche Einladung. |