The Multiple Membrane Problem

Explore the N-membranes problem in this mathematics colloquium talk delivered by Ovidiu Savin from Columbia University. Delve into the equilibrium positions of N ordered elastic membranes subject to forcing and boundary conditions. Examine how the problem can be understood as a system of N-1 coupled obstacle problems with interacting free boundaries that can cross each other. Review free boundary regularity in obstacle-type problems and learn about recent work on the multiple membrane problem, conducted in collaboration with Hui Yu. Gain insights into the special case of N=2, which is equivalent to the classical obstacle problem, and understand its significance in the broader context of membrane dynamics.