Non-local approximation of the Griffith functional

2020/07/09 by Scilla, Giovanni, Solombrino, Francesco
#49J45 #49Q20 #74R10 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2007.04623

Abstract

An approximation, in the sense of Γ-convergence and in any dimension d≥1, 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.

Related

• On some non-local approximation of nonisotropic Griffith-type functionals
• Non-local functionals, total variation, and Gamma-convergence with respect to area-strict convergence
• Gamma-convergence of nonlocal energies for partitions
• Non-local functionals related to the total variation and connections\n with Image Processing
• Local behaviour of the mixed local and nonlocal problems with nonstandard growth