On the local boundedness of generalized minimizers of variational problems with linear growth

TL;DR

This paper proves that generalized solutions to a broad class of linear growth variational problems, including minimal surface and image denoising models, are locally bounded using a Moser iteration technique.

Contribution

It establishes local boundedness of solutions for variational problems with linear growth, extending results to boundary value and image analysis models.

Findings

Generalized solutions are locally bounded.

Applicable to minimal surface and TV-regularization models.

Uses Moser iteration for proof.

Abstract

We prove local boundedness of generalized solutions to a large class of variational problems of linear growth including boundary value problems of minimal surface type and models from image analysis related to the procedure of TV-regularization occurring in connection with the denoising of images, which might even be coupled with an inpainting process. Our main argument relies on a Moser-type iteration procedure.