JournalsifbVol. 9 , No. 1DOI 10.4171/ifb/158

Asymptotic analysis of Mumford–Shah type energies in periodically perforated domains

  • Matteo Focardi

    Università degli Studi di Firenze, Italy
  • Maria Stella Gelli

    Università di Pisa, Italy
Asymptotic analysis of Mumford–Shah type energies in periodically perforated domains cover

Abstract

We study the asymptotic limit of obstacle problems for Mumford-Shah type functionals with pp-growth in periodically-perforated domains \emph{via} the Γ\Gamma-convergence of the associated free-discontinuity energies. In the limit a non-trivial penalization term related to the 11-capacity of the reference hole appears if and only if the size of the perforation scales like \epsnn1\eps^{\frac n{n-1}}, being \eps\eps its periodicity. We give two different formulations of the obstacle problem to include also perforations with Lebesgue measure zero.