Calculus of Variations and Geometric Measure Theory

E. Tasso

On the continuity of the trace operator in $GSBV(\Omega)​​$ and $GSBD(\Omega)$​​

created by tasso on 18 Sep 2018
modified on 26 Jun 2019


Accepted Paper

Inserted: 18 sep 2018
Last Updated: 26 jun 2019

Journal: ESAIM: COCV
Year: 2018


In this paper we present a new result of continuity for the trace operator acting on functions that might jump on a prescribed $(n-1)$-dimensional set $\Gamma$, with the only hypothesis of being rectifiable and of finite measure. We also show an application of our result in relation to the variational model of elasticity with cracks, when the associated minimum problems are coupled with Dirichlet and Neumann boundary conditions.