Yu Yuan, UW

Tuesday, March 28, 2023 - 1:30pm to 3:30pm

PDL C-401

We present an integral approach to the classical Hessian estimates for the

Monge-Ampere equation, originally obtained via a pointwise argument by Pogorelov.

The monotonicity employed here results from a maximal surface interpretation of

"gradient" graph of solutions in pseudo-Euclidean space.

In the introductory part of the talk, we explain the key role of a priori estimates for the

solvability, regularity, rigidity, and error control of numerical approximation for solutions

to partial differential equations such as the Laplace and minimal surface equations.