Return to search

Optimal transport, free boundary regularity, and stability results for geometric and functional inequalities

We investigate stability for certain geometric and functional inequalities and address the regularity of the free boundary for a problem arising in optimal transport theory. More specifically, stability estimates are obtained for the relative isoperimetric inequality inside convex cones and the Gaussian log-Sobolev inequality for a two parameter family of functions. Thereafter, away from a ``small" singular set, local C^{1,\alpha} regularity of the free boundary is achieved in the optimal partial transport problem. Furthermore, a technique is developed and implemented for estimating the Hausdorff dimension of the singular set. We conclude with a corresponding regularity theory on Riemannian manifolds. / text

Identiferoai:union.ndltd.org:UTEXAS/oai:repositories.lib.utexas.edu:2152/20631
Date01 July 2013
CreatorsIndrei, Emanuel Gabriel
Source SetsUniversity of Texas
Languageen_US
Detected LanguageEnglish
Formatapplication/pdf

Page generated in 0.0016 seconds