Borderline Sobolev Inequalities on Symmetric Spaces with Applications

Explore a 51-minute lecture on borderline Sobolev inequalities on symmetric spaces and their applications, delivered by Sagun Chanillo as part of the Hausdorff Trimester Program: Evolution of Interfaces. Delve into the Bourgain-Brezis estimate for the equation −∆u = f, where f is a divergence-free vector field, and discover how this estimate extends to non-compact globally symmetric spaces. Learn about the application of the original Bourgain-Brezis inequality to obtain Strichartz inequalities for wave and Schrodinger equations, as well as new estimates for Maxwell equations and 2D incompressible Navier-Stokes flow. Gain insights into the collaborative research conducted with Jean van Schaftingen and Po-lam Yung in this advanced mathematical exploration.