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Nonlinear Analysis

Free boundary regularity for the 3 membranes problem

Ovidiu Savin, Columbia University

Location:  Hill 705
Date & time: Tuesday, 11 February 2020 at 1:40PM - 3:00PM

Abstract: For a positive integer N,
the N-membranes problem describes the equilibrium position of N ordered elastic membranes subject
to forcing and boundary conditions. If the heights of the membranes are described by real functions u_1, u_2,...,u_N, then the problem can be understood as a system of N-1 coupled obstacle problems with interacting
free boundaries which can cross each other. When N=2 there is only one free boundary and the problem is
equivalent to the classical obstacle problem. In my talk I will discuss some recent work in collaboration with Hui Yu about the case when N=3 and there are two interacting free boundaries.

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