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.

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

GELLI, MARIA STELLA
2007

Abstract

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.
Focardi, M; Gelli, MARIA STELLA
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11568/112419
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