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$ C^{1,\alpha}$-interior regularity for minimizers of a class of variational problems with linear growth related to image inpainting


Authors: M. Bildhauer, M. Fuchs and C. Tietz
Original publication: Algebra i Analiz, tom 27 (2015), nomer 3.
Journal: St. Petersburg Math. J. 27 (2016), 381-392
MSC (2010): Primary 49N60, 49Q20
DOI: https://doi.org/10.1090/spmj/1393
Published electronically: March 30, 2016
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Abstract | References | Similar Articles | Additional Information

Abstract: 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.


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Additional Information

M. Bildhauer
Affiliation: Department of Mathematics, Saarland University, P.O. Box 151150, 66041 Saarbrücken, Germany
Email: bibi@math.uni-sb.de

M. Fuchs
Affiliation: Department of Mathematics, Saarland University, P.O. Box 151150, 66041 Saarbrücken, Germany
Email: fuchs@math.uni-sb.de

C. Tietz
Affiliation: Department of Mathematics, Saarland University, P.O. Box 151150, 66041 Saarbrücken, Germany
Email: tietz@math.uni-sb.de

DOI: https://doi.org/10.1090/spmj/1393
Keywords: Image inpainting, variational method, TV-regularization
Received by editor(s): November 20, 2014
Published electronically: March 30, 2016
Dedicated: Dedicated to Professor N. N. Ural’tseva on her jubilee
Article copyright: © Copyright 2016 American Mathematical Society

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