An Extension Theorem in Sbv and an Application to the Homogenization of the Mumford-shah Functional in Perforated Domains
نویسندگان
چکیده
The aim of this paper is to prove the existence of extension operators for SBV functions from periodically perforated domains. This result will be the fundamental tool to prove the compactness in a non coercive homogenization problem.
منابع مشابه
Homogenization of the Neumann Problem in Perforated Domains: an Alternative Approach
The main goal of this paper is a compactness result for families of functions in the space SBV (Special functions of Bounded Variation) defined on periodically perforated domains. Given an open and bounded set Ω ⊆ R, and an open, connected, and (−1/2, 1/2)-periodic set P ⊆ R, consider for any ε > 0 the perforated domain Ωε := Ω ∩ εP . Let (uε) ⊂ SBV (Ωε), p > 1, be such that ́ Ωε |∇uε|p dx+H(Suε...
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