# Joint IAS/PU Analysis Seminar

## An Energy Model for Harmonic Graphs with Junctions

We consider an energy model for N ordered elastic membranes subject to forcing and boundary conditions. The heights of the membranes are described by real functions u_1, u_2,...,u_N, which minimize an energy functional involving the Dirichlet integral and a potential term depending on the cardinality of the set {u_1,..,u_N}. The potential term corresponds to the physical situation when consecutive membranes are glued to each other on their coincidence set. The problem can be understood as a system of N-1 coupled one-phase free boundary problems with interacting free boundaries.

I will review the known results in the scalar case, and discuss the free boundary regularity when dealing with 3 or more membranes (joint with D. De Silva.)

### Date & Time

April 19, 2024 | 4:00pm – 5:00pm

### Location

Simonyi Hall 101 and Remote Access### Speakers

Ovidiu Savin, Columbia University