Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4589693 | Journal of Functional Analysis | 2016 | 20 Pages |
Abstract
We demonstrate that C2,αC2,α estimates for the Monge–Ampère equation depend in a highly nonlinear way both on the CαCα norm of the right-hand side and 1/α1/α. First, we show that if a solution is strictly convex, then the C2,αC2,α norm of the solution depends polynomially on the CαCα norm of the right-hand side. Second, we show that the C2,αC2,α norm of the solution is controlled by exp((C/α)log(1/α))exp((C/α)log(1/α)) as α→0α→0. Finally, we construct a family of solutions in two dimensions to show the sharpness of our results.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Alessio Figalli, Yash Jhaveri, Connor Mooney,