Geodesic
Asymptotic analysis of Mumford–Shah type energies in periodically perforated domains
Matteo Focardi1 orcid ; Maria Stella Gelli2
1Università degli Studi di Firenze, Italy
2Università di Pisa, Italy
Interfaces and free boundaries, Tome 9 (2007) no. 1, pp. 107-132

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DOI

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−1n​, being ε its periodicity. We give two different formulations of the obstacle problem to include also perforations with Lebesgue measure zero.
DOI : 10.4171/ifb/158
Classification : 35-XX, 65-XX, 76-XX, 92-XX

Matteo Focardi  1   ; Maria Stella Gelli  2

1 Università degli Studi di Firenze, Italy
2 Università di Pisa, Italy 
Matteo Focardi; Maria Stella Gelli. Asymptotic analysis of Mumford–Shah type energies in periodically perforated domains. Interfaces and free boundaries, Tome 9 (2007) no. 1, pp. 107-132. doi: 10.4171/ifb/158
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     title = {Asymptotic analysis of {Mumford{\textendash}Shah} type energies in periodically perforated domains},
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     pages = {107--132},
     year = {2007},
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     doi = {10.4171/ifb/158},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/158/}
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