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.
(McCann, R., Rakshit, A.) Discontinuities in optimal transport between nonconvex domains, Preprint, [arXiv]
(Rakshit, A., Wu, D.) Geometric Viewpoint of L^∞ Estimates for Linearized Monge-Ampère Equations, Preprint, [arXiv]
(Rakshit, A., Sen, A.) Solutions to Monge-Ampère Equations with Low Codimensional singularities, Preprint, [arXiv]
(Rakshit, A.) Pointwise Schauder estimates for optimal transport maps of rough densities. Discrete Contin. Dyn. Syst. 2025, [arXiv][Journal]
(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]