Optimal boundary regularity for a singular Monge-Ampère equation
Abstract
In this paper we study the optimal global regularity for a singular Monge-Ampère type equation which arises from a few geometric problems. We find that the global regularity does not depend on the smoothness of domain, but it does depend on the convexity of the domain. We introduce (a , η) type to describe the convexity. As a result, we show that the more convex is the domain, the better is the regularity of the solution. In particular, the regularity is the best near angular points.
- Publication:
-
Journal of Differential Equations
- Pub Date:
- June 2018
- DOI:
- 10.1016/j.jde.2018.01.051
- Bibcode:
- 2018JDE...264.6873J
- Keywords:
-
- 35J60;
- 35J69;
- 53A15;
- 53C45