# C^1,α regularity of variational problems with a convexity constraint

arxiv（2024）

摘要

In this paper, we establish the interior C^1,α regularity of
minimizers of a class of functionals with a convexity constraint, which
includes the principal-agent problems studied by Figalli-Kim-McCann (J.
Econom. Theory 146 (2011), no. 2, 454-478). The C^1,1 regularity
was previously proved by Caffarelli-Lions in an unpublished note when the cost
is quadratic, and recently extended to the case where the cost is uniformly
convex with respect to a general preference function by
McCann-Rankin-Zhang(arXiv:2303.04937v3). Our main result does not
require the uniform convexity assumption on the cost function. In particular,
we show that the solutions to the principal-agent problems with q-power cost
are C^1,1/q-1 when q > 2 and C^1,1 when 1

更多

查看译文

AI 理解论文

溯源树

样例

生成溯源树，研究论文发展脉络

Chat Paper

正在生成论文摘要