Calculus of Variations and Geometric Measure Theory

V. Crismale

Density in $SBD$ and approximation of fracture energies

created by crismale on 21 Feb 2019
modified on 13 Dec 2019


Published Paper

Inserted: 21 feb 2019
Last Updated: 13 dec 2019

Journal: Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl.
Volume: 30
Number: 3
Pages: 533-542
Year: 2019
Doi: 10.4171/RLM/859


We prove three density theorems, in the strong $BD$ topology, for the three subspaces of $SBD$ functions: $SBD$; $SBD^p_\infty$, where the absolutely continuous part of the symmetric gradient is in $L^p$, with $p>1$; $SBD^p$, whose functions are in $SBD^p_\infty$ and the jump set has finite $\mathcal{H}^{n-1}$-measure. We compare them with existing results, discussing related approximation of fracture energies.