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VAPS 1: 'Free boundary regularity for the 3 membranes problem'
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Speaker: Ovidiu Savin, Columbia University
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. I will review some of the regularity theory for the standard obstacle problem, and then discuss some recent work in collaboration with Hui Yu about the case when N=3 and there are two interacting free boundaries.
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. I will review some of the regularity theory for the standard obstacle problem, and then 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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