Geodesic
$C^{1,\alpha}$-interior regularity for minimizers of a~class of variational problems with linear growth related to image inpainting
Algebra i analiz, Tome 27 (2015) no. 3, pp. 51-65.

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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 $C^{1,\alpha}$ interior differentiability of solutions of this new variational problem.
Keywords: image inpainting, variational method, TV-regularization. 
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M. Bildhauer; M. Fuchs; C. Tietz. $C^{1,\alpha}$-interior regularity for minimizers of a~class of variational problems with linear growth related to image inpainting. Algebra i analiz, Tome 27 (2015) no. 3, pp. 51-65. http://geodesic.mathdoc.fr/item/AA_2015_27_3_a2/

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