Asymptotic analysis of Mumford–Shah type energies in periodically perforated domains
Asymptotic analysis of Mumford–Shah type energies in periodically perforated domains
复制标题
周期性穿孔域中 Mumford-Shah 型能量的渐近分析
DOI：
10.4171/ifb/158
复制
发表时间：
2007
影响因子：
1
通讯作者：
M. Gelli
中科院分区：
文献类型：
--
作者：
M. Focardi;M. Gelli
利用伴随的自由间断能的Γ-收敛性质，研究了周期穿孔区域上具增长的Mumford-Shah型泛函的障碍问题的渐近极限。在极限中，当且仅当穿孔的尺寸如En/(n−1)，e为其周期性时，才出现与参考孔的1-容量有关的非平凡惩罚项。我们给出了障碍问题的两种不同的公式，以包括具有勒贝格测度为零的穿孔。
We study the asymptotic limit of obstacle problems for Mumford–Shah type functionals with pgrowth 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 en/(n−1), e being its periodicity. We give two different formulations of the obstacle problem to include also perforations with Lebesgue measure zero.