Uploaded January 2024 | Updated September 2026, 3 weeks ago
Abstract: A couple of years ago, with M. Goldman we devised a new approach to the regularity theory for Optimal Transportation that mimics De Giorgi's approach to the regularity theory of minimal surfaces in the sense that a harmonic approximation result is at its center: Under a non-dimensional smallness condition, the displacement is close to the gradient of a harmonic function.
Probably the main advantage of this variational regularity theory over the one based on maximum principle — and attached to the name of Caffarelli — is that it does not require any regularity of the involved measures. Hence it can be applied to the popular matching problem, where it provides regularity on large scales
This lecture was part of the bi-annual Abel Symposium.
This year the title of the symposium was Partial Differential Equations waves, Nonlinearities and Nonlocalities.
The symposium was funded by
- The Norwegian Academy of Sciences and Letters via the Abel board and The Norwegian Mathematical Society
- NTNU Norwegian University of Science and Technology
- Research Council of Norway via the grant Waves and Nonlinear Phenomena
- Trond Mohn Foundation
Abstract: A couple of years ago, with M. Goldman we devised a new approach to the regularity theory for Optimal Transportation that mimics De Giorgi's approach to the regularity theory of minimal surfaces in the sense that a harmonic approximation result is at its center: Under a non-dimensional smallness condition, the displacement is close to the gradient of a harmonic function.
Probably the main advantage of this variational regularity theory over the one based on maximum principle — and attached to the name of Caffarelli — is that it does not require any regularity of the involved measures. Hence it can be applied to the popular matching problem, where it provides regularity on large scales
This lecture was part of the bi-annual Abel Symposium.
This year the title of the symposium was Partial Differential Equations waves, Nonlinearities and Nonlocalities.
The symposium was funded by
- The Norwegian Academy of Sciences and Letters via the Abel board and The Norwegian Mathematical Society
- NTNU Norwegian University of Science and Technology
- Research Council of Norway via the grant Waves and Nonlinear Phenomena
- Trond Mohn Foundation
