We study the asymptotic limit of obstacle problems for Mumford–Shah type functionals with p- growth in periodically perforated domains via the Γ -convergence of the associated free-discontinuity energies. In the limit a non-trivial penalization term related to the 1-capacity of the reference hole appears if and only if the size of the perforation scales like εn/(n−1) , ε being its periodicity. We give two different formulations of the obstacle problem to include also perforations with Lebesgue measure zero.
|Autori:||FOCARDI M; GELLI M|
|Titolo:||Asymptotic analysis of Mumford-Shah type energies in periodically-perforated domains|
|Anno del prodotto:||2007|
|Digital Object Identifier (DOI):||10.4171/IFB/158|
|Appare nelle tipologie:||1.1 Articolo in rivista|