Người báo cáo:
Thời gian, địa điểm: 9h300, Phòng 4 nhà A14 - Viện Toán học
Tóm tắt: These lectures will be concerned with the linearized Monge-Ampere equation, its regularity and geometric applications. Linearized Monge-Ampere equation is an interesting combination of the linear elliptic equation and the Monge-Ampere equation. Though highly degenerate, linearized Monge-Ampere equation shares many regularity results as those of the Poisson equation. Though linear, it has the same challenging aspects of the fully nonlinear Monge-Ampere equation. We will start from the fundamental Holder regularity result of Caffarelli-Gutierrez to recent developments regarding higher regularity in the interior and up to the boundary. We will also describe applications to fourth order, fully nonlinear geometric partial differential equations such as affine maximal surface and Abreu equations in affine and complex geometry. |
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