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\(C^{1,\alpha}\)-interior regularity for minimizers of a class of variational problems with linear growth related to image inpainting. (English) Zbl 1335.49058
St. Petersbg. Math. J. 27, No. 3, 381-392 (2016) and Algebra Anal. 27, No. 3, 51-65 (2015).
Summary: 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.
Reviewer: Reviewer (Berlin)

49N60 Regularity of solutions in optimal control
49Q20 Variational problems in a geometric measure-theoretic setting
94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
Full Text: DOI
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