Analysis Seminar

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Gamma-convergence for the plane-to-wrinkles transition problem

Speaker: Roberta Marziani, Universita di Siena

Location: Warren Weaver Hall 1302

Date: Thursday, February 13, 2025, 11 a.m.

Synopsis:

Motivated by physical experiments, we consider a variational problem modelling transition between flat and wrinkled region in a thin elastic sheet. We start with a description of the model and of some related results. We then perform an asymptotic analysis, via $\Gamma$-concergence, as the sheet thickness goes to 0.  The limiting problem is scalar and convex, but constrained and posed for measures. For the lower bound we first pass to quadratic variables so that the constraint becomes linear, and then obtain the lower bound by Reshetnyak’s theorem. The construction of the recovery sequence for the upper bound relies on mollification of quadratic variables, and careful choice of multiple construction parameters. Eventually for the limiting problem we show existence of a minimizer and equipartition of the energy for each frequency. This is based on a joint work with Peter Bella (TU Dortmund).