Calculus of Variations and Geometric Measure Theory

J. F. Babadjian - G. A. Francfort

Continuity equation and characteristic flow for scalar Hencky plasticity

created by babadjian on 15 May 2020
modified on 19 Apr 2021


Accepted Paper

Inserted: 15 may 2020
Last Updated: 19 apr 2021

Journal: Comm. Pure Appl. Math.
Year: 2021


We investigate uniqueness issues for a continuity equation arising out of the simplest model for plasticity, Hencky plasticity. The associated system is of the form $\rm{ curl\;}(\mu\sigma)=0$ where $\mu$ is a nonnegative measure and $\sigma$ a two-dimensional divergence free unit vector field. After establishing the Sobolev regularity of that field, we provide a precise description of all possible geometries of the characteristic flow, as well as of the associated solutions.