Calculus of Variations and Geometric Measure Theory

G. Scilla - F. Solombrino

Non-local approximation of the Griffith functional

created by scilla on 09 Jul 2020
modified by solombrin on 02 Mar 2021


Published Paper

Inserted: 9 jul 2020
Last Updated: 2 mar 2021

Journal: NoDEA Nonlinear Differential Equations Appl.
Volume: 28
Pages: Art. 17
Year: 2021
Doi: 10.1007/s00030-021-00682-y

ArXiv: 2007.04623 PDF


An approximation, in the sense of $\Gamma$-convergence and in any dimension $d\geq1$, of Griffith-type functionals, with $p-$growth ($p>1$) in the symmetrized gradient, is provided by means of a sequence of non-local integral functionals depending on the average of the symmetrized gradients on small balls.

Keywords: Brittle fracture, $\Gamma$-convergence, Griffith functional, non-local approximations