seminar: Multiwell problems in nonlinear elasticity
speaker: Sergio Conti (Universität Bonn)abstract: Variational models in nonlinear elasticity have the form $I(u)=\int W(Du)dx$, where $u:\Omega\subset\mathbb{R}n\to\mathbb{R}n$ is the deformation and $W:\mathbb{R}{n\times n}\to0,\infty$ the elastic energy density. In the study of solid-solid phase transitions one considers the case that $W$ vanishes on a set of the form $SO(n)A1\cup\dots SO(n)Al$, with $A1,\dots Al$ being the eigenstrains for the different phases. Focusing on the three-well problem in three dimensions, we show that for many boundary conditions the functional $I$ has infinitely many minimizers which are nowhere regular. We then show that if a singular perturbation is included, low-energy states become much more rigid and different qualitative properties are expected. The talk is based on joint work with Milena Chermisi, Georg Dolzmann, and Bernd Kirchheim.
timetable:
Thu 15 Nov, 16:45 - 17:30, Sala Conferenze Centro De Giorgi
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