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A monotonicity approach to Pogorelov's Hessian estimates for Monge-Ampere equation

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.
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