The Monge-Ampere System - Convex Integration in Arbitrary Dimension and Codimension
Explore the flexibility of weak solutions to the Monge-Ampere system through convex integration in this 55-minute lecture by Marta Lewicka at the Hausdorff Center for Mathematics. Delve into the natural extension of the Monge-Ampere equation in the contexts of isometric immersions and nonlinear elasticity. Discover the main technical ingredient, the "stage" construction, which achieves Holder regularity C^(1,α) of approximating fields for arbitrary dimensions and codimensions. Learn how this construction applies to the isometric immersion problem, recovering and quantifying previous results. Examine topics such as isometric interference, flexibility, and perturbation while gaining insights into the general theorem and its implications for mathematical research.