Calculus of Variations and Geometric Measure Theory

M. Friedrich

A Korn-Poincare-type inequality for special functions of bounded deformation

created by friedrich on 26 Jun 2015



Inserted: 26 jun 2015
Last Updated: 26 jun 2015

Year: 2015


We present a Korn-Poincare-type inequality in a planar setting which is in the spirit of the Poincare inequality in SBV due to De Giorgi, Carriero, Leaci. We show that for each function in SBD$^2$ one can find a modification which differs from the original displacement field only on a small set such that the distance of the modification from a suitable infinitesimal rigid motion can be controlled by an appropriate combination of the elastic and the surface energy. In particular, the result can be used to obtain compactness estimates for functions of bounded deformation.

Keywords: free discontinuity problems, Functions of Bounded Deformation, Brittle materials, variational fracture , Korn-Poincare-inequality