This $252,563.00 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program supports research on singular higher-order linearized Monge-Ampère type equations with drifts. The project, led by researchers at Indiana University, Bloomington, aims to investigate the solvability, regularity properties, and asymptotic behavior of these equations, which have applications in complex geometry, meteorology, economics, elasticity, physics, and the calculus of variations. The research will focus on three main themes: solvability of singular affine maximal surface and Abreu equations with drifts, establishing higher-order derivative estimates for singular linearized Monge-Ampère equations, and studying the solvability of singular Abreu equations with degenerate boundary data. The project, which runs from Jul 15, 2025 to Jun 30, 2028, is expected to advance the understanding of nonlinear partial differential equations and provide novel approaches to regularity theory, while also mentoring graduate students and engaging undergraduate students in mathematical research.
Mod # | Description | Reason For Modification | Federal Obligation (Click to sort descending) | Date (Click to sort ascending) |
|---|---|---|---|---|
| Not listed | $252.6k | 7/7/25 |