Inserted: 4 mar 2018
Last Updated: 1 oct 2019
Journal: Discrete Contin. Dyn. Syst. A
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 $1$.