My research interests are in Optimal Transport and Partial Differential Equations. In particular, I’m interested in Monge-Ampere type equations that comes from optimal transport. Also, I’m interested in dynamic setting of optimal transport problem and its gradient flow structure.
- Holder regularity of solutions to generated Jacobian equations
- Pure and Applied Analysis 3-1 (2021), 163–188. DOI 10.2140/paa.2021.3.163
- In this paper, I generalized local Holder regularity result of G.Loeper(https://arxiv.org/abs/math/0504137) to generated Jacobian equation case.
- Synthetic MTW conditions and their equivalence under mild regularity assumption on the cost function
- ArXiv : https://arxiv.org/abs/2010.14471
- In this paper, I show Loeper’s condition and quantitatively quasi-convexity are equivalent when the cost function is C^2 with Lipschitz mixed hessian.