Remarks on some minimization problems associated with BV norms
Haïm Brézis · Discrete and Continuous Dynamical Systems · 2019
The purpose of this paper is twofold. Firstly I present an optimal regularity result for minimizers of a $ 1D $ convex functional involving the BV-norm, under Neumann boundary condition. This functional is a simplified version of models occuring in Image Processing. Secondly I investigate the existence of minimizers for the same functional under Dirichlet boundary condition. Surprisingly, this turns out to be a delicate issue, which is still widely open.