My work is broadly in the area of elliptic partial differential equations (PDEs). I use tools from geometric analysis and calculus of variations to understand regularity (good behavior) and singularities (bad behavior) of solutions to these equations.
(Rakshit, A.) Pointwise Schauder estimates for optimal transport maps of rough densities. Preprint: 2024, [arXiv]
(Mooney, C. , Rakshit, A.) Sobolev regularity for optimal transport maps of non-convex planar domains. SIAM Journal on Mathematical Analysis, 2024, [arXiv], [Journal]
(Mooney, C. , Rakshit, A.) Singular structures in solutions to the Monge-Ampère equation with point masses. Math. Eng., 2022, [arXiv],[Journal]