Our goal is to construct a new metric, which renders this flow uniformly Lipschitz continuous on bounded subsets of $H^1$. For this purpose, $H^1$ is given the structure of a Finsler manifold, where the norm of tangent vectors is defined in terms of an optimal transportation problem. For paths of piecewise smooth solutions, one can carefully estimate how the weighted length grows in time.
To complete the construction, one needs an additional argument showing that the family of piecewise smooth solutions is dense. This generic regularity property can be proved using a variable transformation that reduces the equations to a semilinear system, followed by an application of Thom's transversality theorem.
http://cvgmt.sns.it/seminar/487/
When | Tue Nov 24, 2015 4pm – 5pm Coordinated Universal Time |
Where | Dipartimento di Matematica (Sala Riunioni) (map) |