A variant of the Geman–McClure model for image restoration

We study existence and regularity of the solutions for the variant of the Geman–McClure model for image restoration introduced by Chipot, March, Rosati and Vergara Caffarelli. We generalize their one-dimensional existence result to dimensions n⩾2n⩾2. Our argumentation is fairly simple and essentially different from the one in Chipot et al. (1997) [4]. We also show that the minimizers are continuous.