Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	周斌研究员,北京大学
Inviter:	彭发
Title:	Singular Abreu equations and linearized Monge-Ampère equations with drifts
Language:	English&Chinese
Time & Venue:	2023.05.17 15:00-16:00 腾讯会议：896-246-072
Abstract:	We study the solvability of singular Abreu equations which arise in the approximation of convex functionals subject to a convexity constraint. Previous works established the solvability of their second boundary value problems either in two dimensions, or in higher dimensions under either a smallness condition or a radial symmetry condition. Here, we solve the higher dimensional case by transforming singular Abreu equations into linearized Monge-Ampère equations with drifts. We establish global H?lder estimates for the linearized Monge-Ampère equation with drifts under suitable hypotheses, and then use them to the regularity and solvability of the second boundary value problem for singular Abreu equations in higher dimensions. Many cases with general right-hand side will also be discussed.