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

created by tasso on 18 Sep 2018

[BibTeX]

Submitted Paper

Inserted: 18 sep 2018
Last Updated: 18 sep 2018

Year: 2018
Notes:

Preprint SISSA 39$/$2018$/$MATE

Abstract:

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.