◆ Annali dell'Universita di Ferrara. Sezione 7, Scienze matematiche. Universita di Ferrara2026-01-01
A De Giorgi conjecture on the regularity of minimizers of Cartesian area in 1D.
Giovanni Bellettini, Shokhrukh Yu Kholmatov
原始摘要（英文原文）· Original abstract
We prove a C 1 , 1 -regularity result for minimizers of the functional ∫ I 1 + | D u | 2 + ∫ I | u - g | d s , u ∈ B V ( I ) , provided I ⊂ R is a bounded open interval and ‖ g ‖ ∞ is sufficiently small, thus partially establishing a De Giorgi conjecture in dimension one and codimension one. We also extend our result to a suitable anisotropic setting.