caa a22 4500 605523746 CHVBK 20210128100751.0 cr unu---uuuuu 210128e20151001xx s 000 0 eng 10.1007/s10958-015-2575-2 doi (NATIONALLICENCE)springer-10.1007/s10958-015-2575-2 Existence of Generalized Minimizers and Dual Solutions for a Class of Variational Problems with Linear Growth Related to Image Recovery [Elektronische Daten] [M. Fuchs, C. Tietz] We continue the analysis of modifications of the total variation image inpainting method formulated on the space BV (Ω) M and treat the case of vector-valued images where we do not impose any structure condition on the density F and the dimension of the domain Ω is arbitrary. We discuss the existence of generalized solutions of the corresponding variational problem and show the unique solvability of the associated dual variational problem. We establish the uniqueness of the absolutely continuous part ∇ a u of the gradient of BV -solutions u on the domain Ω and get the uniqueness of BV -solutions outside the damaged region D. We also prove new density results for functions of bounded variation and for Sobolev functions. Bibliography: 36 titles. Springer Science+Business Media New York, 2015 Fuchs M. Universität des Saarlandes, Fachbereich 6.1 Mathematik, Postfach 15 11 50, D-66041, Saarbrücken, Germany aut Tietz C. Universität des Saarlandes, Fachbereich 6.1 Mathematik, Postfach 15 11 50, D-66041, Saarbrücken, Germany aut Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 210/4(2015-10-01), 458-475 1072-3374 210:4<458 2015 210 10958 https://doi.org/10.1007/s10958-015-2575-2 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10958-015-2575-2 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Fuchs M. Universität des Saarlandes, Fachbereich 6.1 Mathematik, Postfach 15 11 50, D-66041, Saarbrücken, Germany aut NATIONALLICENCE 700 1- Tietz C. Universität des Saarlandes, Fachbereich 6.1 Mathematik, Postfach 15 11 50, D-66041, Saarbrücken, Germany aut NATIONALLICENCE 773 0- Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 210/4(2015-10-01), 458-475 1072-3374 210:4<458 2015 210 10958