View article

We study energy minimizing properties of the function [Formula: see text] , where [Formula: see text] is the solution to the [Formula: see text] -Laplacian Dirichlet problem with prescribed boundary values. Here p:Ω→[1,∞) is a variable exponent and [Formula: see text] for λ_j>1. This problem leads in a natural way to a mixture of Sobolev and total variation norms. The main results are obtained under the assumption that p is strongly log-Hölder continuous and bounded. To motivate our approach we also consider the one-dimensional case and give examples which justify our assumptions. The results can be applied in the analysis of a model for image restoration combining total variation and isotropic smoothing.