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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.
|Number of pages||15|
|Journal||Discrete and Continuous Dynamical Systems- Series A|
|Publication status||Published - Jun 2019|