$C^{1,\alpha }$-interior regularity for minimizers of a class of variational problems with linear growth related to image inpainting
Michael Bildhauer, Michael Fuchs, C. Tietz · St Petersburg Mathematical Journal · 2016
A modification of the total variation image inpainting method is investigated. By using DeGiorgi type arguments, the partial regularity results established previously are improved to the $C^{1,\alpha }$ interior differentiability of solutions of this new variational problem.