Abstract: In models of Nonlinear Elasticity, the natural physical deformation is a minimizer of an energy functional containing the integral of |Df(x)|^p, and we search for the minimizer in the Sobolev space W^{1,p}(Omega, R^n). In the previous results, one assumes that p is at least n-1 to ensure the non-interpenetration of matter.
In this talk we prove the lower semicontinuity of an energy functional that allows, for the first time, for p<n-1. Our class of admissible deformations consists of weak limits of Sobolev homeomorphisms. We also introduce a model that allows for cavitations by studying weak limits of homeomorphisms that can open cavities at some points. In that model we add the measure of the created surface to the energy functional and we again prove lower semicontinuity.
This is a joint work with Daniel Campbell and Stanislav Hencl.
Geometric analysis seminar: Anna Doležalová (Czech Academy of Sciences)
Event information
Event date
-
Event type
Public lectures, seminars and round tables
Event language
English
Event payment
Free of charge
