Calculus of Variations and Geometric Measure Theory

A. Cesaroni - S. Dipierro - M. Novaga - E. Valdinoci

Minimizers of the $p$-oscillation functional

created by novaga on 04 Mar 2018
modified on 01 Oct 2019


Published Paper

Inserted: 4 mar 2018
Last Updated: 1 oct 2019

Journal: Discrete Contin. Dyn. Syst. A
Volume: 39
Number: 12
Pages: 6785-6799
Year: 2019

ArXiv: 1803.01371 PDF


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 $1$.