Minimizers of the $ p $ -oscillation functional
Annalisa Cesaroni, Serena Dipierro, Matteo Novaga, Enrico Valdinoci · Discrete and Continuous Dynamical Systems · 2019
We define a family of functionals, called $ p $-oscillation functionals, that can be interpreted as discrete versions of the classical total variation functional for $ p = 1 $ and of the $ p $-Dirichlet functionals for $ p>1 $. We introduce the notion of minimizers and prove existence of solutions to the Dirichlet problem. Finally we provide a description of Class A minimizers (i.e. minimizers under compact perturbations) in dimension $ 1 $.