Complex Valued Nonlinear PDEs

A 19-minute lecture by Wontae Kim exploring complex valued nonlinear PDEs, presented at the Workshop on "Degenerate and Singular PDEs" held at the Erwin Schrödinger International Institute for Mathematics and Physics (ESI) in February 2025. Delve into the mathematical analysis of complex valued elliptic p-Laplace equations, focusing on their existence, uniqueness, and gradient regularity properties. Learn about the framework established by Cohen, DeVore, and Schwab in their publications from 2010-2015, which extended real-valued linear equations to the complex setting to facilitate numerical results for parametric PDEs.