Calculus of Variations and Geometric Measure Theory

M. Friedrich

A Korn-type inequality in SBD for functions with small jump sets

created by friedrich on 26 Jun 2015



Inserted: 26 jun 2015
Last Updated: 26 jun 2015

Year: 2015


We present a Korn-type inequality in a planar setting for special functions of bounded deformation. We prove that for each function in SBD2 with sufficiently small jump set the distance of the function and its derivative from an infinitesimal rigid motion can be controlled in terms of the linearized elastic strain outside of a small exceptional set of finite perimeter. Particularly the result shows that each function in SBD2 has bounded variation away from an arbitrarily small part of the domain.

Keywords: Functions of Bounded Deformation, Korn's inequality, Brittle materials, variational fracture , Korn-Poincare inequality