2026京师调和分析论坛(9) (2026.10.14)
会议安排
Zoom会议号：891 378 08543，入会密码：999999
时间 |
报告人 |
报告题目 |
单位 |
15:00-15:45 |
Óscar Domínguez |
Extrapolation Methods for $\Gamma$-Convergence and Applications to Image Processing (I) |
CUNEF University-Madrid，西班牙 |
15:55-16:40 |
Extrapolation Methods for $\Gamma$-Convergence and Applications to Image Processing (II) |
会议由以下项目支持:
北京师范大学教育部&科技部“调和分析及其应用创新引智基地”
国家自然科学基金重点项目“相关于球平均、Chirp函数和区域上算子的函数空间公理化实变理论及其应用”
组委会：戴峰, 杨大春, 袁文, 张阳阳
2026年9月30日
报告信息
报告题目: Extrapolation Methods for $\Gamma$-Convergence and Applications to Image Processing
报告摘要: In this talk, we introduce, via the Gagliardo completion, an extrapolation framework within De Giorgi’s Γ-convergence theory and develop its applications to variational problems arising in image processing, in particular, the Rudin–Osher–Fatemi (ROF) model. Special emphasis is given to new tools connecting extrapolation theory and variational analysis, specifically the extrapolation of compactness and the construction of variational K-functionals. These tools allow for the derivation of quantitative rates of convergence of minimizers. As an application, we resolve the inverse regularity problem in ROF: regularity of the observed image that guarantees a prescribed rate of convergence to the solution of ROF is governed by the decay of variational K-functionals, which is explicitly captured by the Brezis–Van Schaftingen–Yung spaces. Moreover, this extrapolation framework provides a unified perspective on several limiting results, including the celebrated Bourgain–Brezis–Mironescu formula and its Γ-convergence counterparts due to Ponce.
