Mission p smaller than n-1: Possible - Nonlinear Elasticity Beyond Conventional Limits

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 $p$ less than $n-1$. 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.

MathematicsPhysics

Audience: researchers in the topic

Nečas Seminar on Continuum Mechanics

Series comments: This seminar was founded on December 14, 1966.

Faculty of Mathematics and Physics, Charles University, Sokolovská 83, Prague 8. If not written otherwise, we will meet on Mondays at 15:40 in lecture hall K3 (2nd floor)