Minimizers of anisotropic Rudin-Osher-Fatemi models  

作　　者：Ruiling JIA Meiyue JIANG 

机构地区：[1]LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, China

出　　处：《Frontiers of Mathematics in China》2015年第6期1355-1388,共34页中国高等学校学术文摘·数学（英文）

基　　金：Acknowledgements The authors thank the referees for careful reading of the paper and useful suggestions which improve the presentation. This work was supported by the National Natural Science Foundation of China （Grant Nos. 11271025, 11371038, 11431001）.

摘　　要：We give the explicit formulas of the minimizers of the anisotropic Rudin-Osher-Fatemi models Eφ1（U）=∫Ωφ°（Du）Dx＋λ∫｜u-f｜dx,u∈BV（Ω） Eφ2（U）=∫Ωφ°（Du）Dx＋λ∫（u-f）2dx,u∈BV（Ω）,where Ω R2 is a domain, φ° is an anisotropic norm on R2, and f is a solution of the anisotropie 1-Laplaeian equations.We give the explicit formulas of the minimizers of the anisotropic Rudin-Osher-Fatemi models Eφ1（U）=∫Ωφ°（Du）Dx＋λ∫｜u-f｜dx,u∈BV（Ω） Eφ2（U）=∫Ωφ°（Du）Dx＋λ∫（u-f）2dx,u∈BV（Ω）,where Ω R2 is a domain, φ° is an anisotropic norm on R2, and f is a solution of the anisotropie 1-Laplaeian equations.

关 键 词：Anisotropic Rudin-Osher-Fatemi （ROF） model Euler-Lagrange equation φ-curvature 

分 类 号：O343.8[理学—固体力学] O177[理学—力学]