Published Paper

Inserted: 27 jan 2006
Last Updated: 2 may 2008

Journal: Inter. Free Boundaries
Volume: 9
Pages: 107-132
Year: 2007

Abstract:

We study the asymptotic limit of obstacle problems for Mumford-Shah type functionals with $p$-growth in periodically-perforated domains via the $\Gamma$-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 $\epsilon^{n/(n-1)}$, being $\eps$ its periodicity. We give two different formulations of the obstacle problem to include also perforations with Lebesgue measure zero.

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