JournalsifbVol. 9, No. 1pp. 107–132

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
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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.

Cite this article

Matteo Focardi, Maria Stella Gelli, Asymptotic analysis of Mumford–Shah type energies in periodically perforated domains. Interfaces Free Bound. 9 (2007), no. 1, pp. 107–132

DOI 10.4171/IFB/158