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., 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]