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All issues Volume 30 (2024) ESAIM: COCV, 30 (2024) 8 References
Open Access
Issue
ESAIM: COCV
Volume 30, 2024
Article Number 8
Number of page(s) 39
DOI https://doi.org/10.1051/cocv/2023090
Published online 09 February 2024
  1. B. Dacorogna, Direct methods in the calculus of variations. Vol. 78 of Applied Mathematical Sciences, 2nd edn. Springer, New York (2008). [Google Scholar]
  2. C. Goffman and J. Serrin, Sublinear functions of measures and variational integrals. Duke Math. J. 31 (1964) 159–178. [CrossRef] [MathSciNet] [Google Scholar]
  3. A. Chambolle and P.L. Lions, Image recovery via total variation minimization and related problems. Numer. Math. 76 (1997) 167-188. [CrossRef] [MathSciNet] [Google Scholar]
  4. L. Rudin, S. Osher and E. Fatemi, Nonlinear total variation based noise removal algorithms. Physica D: Nonlinear Phenomena 60 (1992) 259–268. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  5. M. Genzel, M. Marz and R. Seidel, Compressed sensing with 1D total variation: Breaking sample complexity barriers via non-uniform recovery. Inform. Inference 11 (2021) 203–250. [Google Scholar]
  6. T. Miyata and Y. Sakai, Vectorized total variation defined by weighted l infinity norm for utilizing inter channel dependency, in 2012 19th IEEE International Conference on Image Processing (2012) 3057–3060. [CrossRef] [Google Scholar]
  7. A. Chambolle and T. Pock, A first-order primal-dual algorithm for convex problems with applications to imaging. J. Math. Imaging Vis. 40 (2011) 120–145. [CrossRef] [Google Scholar]
  8. M. Bonforte and A. Figalli, Total variation flow and sign fast diffusion in one dimension. J. Differ. Equ. 252 (2012) 4455–4480. [CrossRef] [Google Scholar]
  9. A. Briani, A. Chambolle, M. Novaga and G. Orlandi, On the gradient flow of a one-homogeneous functional. Confluentes Math. 3 (2011) 617–635. [CrossRef] [Google Scholar]
  10. P.B. Mucha and P. Rybka, A note on a model system with sudden directional diffusion. J. Stat. Phys. 146 (2012) 975–988. [CrossRef] [MathSciNet] [Google Scholar]
  11. A. Nakayasu and P. Rybka, Integrability of the derivative of solutions to a singular one-dimensional parabolic problem. Topol. Methods Nonlinear Anal. 52 (2018) 239–257. [MathSciNet] [Google Scholar]
  12. F. Alter, V. Caselles and A. Chambolle, Evolution of characteristic functions of convex sets in the plane by the minimizing total variation flow. Interfaces Free Bound. 7 (2005) 29–53. [CrossRef] [MathSciNet] [Google Scholar]
  13. L. Ambrosio, N. Fusco and D. Pallara, Functions of bounded variation and free discontinuity problems. Oxford Mathematical Monographs. The Clarendon Press, Oxford University Press, New York (2000). [CrossRef] [Google Scholar]
  14. V. Caselles, K. Jalalzai and M. Novaga, On the jump set of solutions of the total variation flow. Rend. Semin. Mat. Univ. Padova 130 (2013) 155–168. [CrossRef] [MathSciNet] [Google Scholar]
  15. V. Caselles, A. Chambolle and M. Novaga, The discontinuity set of solutions of the TV denoising problem and some extensions. Multiscale Model. Simul. 6 (2007) 879–894. [CrossRef] [MathSciNet] [Google Scholar]
  16. T. Valkonen, The jump set under geometric regularization. Part 1: basic technique and first-order denoising. SIAM J. Math. Anal. 47 (2015) 2587–2629. [CrossRef] [MathSciNet] [Google Scholar]
  17. S. Moll, The anisotropic total variation flow. Math. Ann. 332 (2005) 177–218. [CrossRef] [MathSciNet] [Google Scholar]
  18. M. Lasica, S. Moll and P.B. Mucha, Total variation denoising in l1 anisotropy. SIAM J. Imaging Sci. 10 (2017) 1691–1723. [CrossRef] [MathSciNet] [Google Scholar]
  19. M. Lasica and P. Rybka, Existence of W1,1 solutions to a class of variational problems with linear growth on convex domains. Indiana Univ. Math. J. 70 (2021) 2427–2450. [CrossRef] [MathSciNet] [Google Scholar]
  20. L. Giacomelli and M. Lasica, A local estimate for vectorial total variation minimization in one dimension. Nonlinear Anal. 181 (2019) 141–146. [CrossRef] [MathSciNet] [Google Scholar]
  21. G. Mercier, Continuity results for TV-minimizers. Indiana Univ. Math. J. 67 (2018) 1499–1545. [CrossRef] [MathSciNet] [Google Scholar]
  22. A. Chambolle and M. Novaga, Existence and uniqueness for planar anisotropic and crystalline curvature flow, in Variational methods for evolving objects. Vol. 67 of Adv. Stud. Pure Math.. Math. Soc. Japan [Tokyo] (2015) 87-113. [Google Scholar]
  23. F. Demengel and R. Temam, Convex functions of a measure and applications. Indiana Univ. Math. J. 33 (1984) 673–709. [CrossRef] [MathSciNet] [Google Scholar]
  24. L.C. Evans and R.F. Gariepy, Measure theory and fine properties of functions. Studies in Advanced Mathematics. CRC Press, Boca Raton, FL (1992). [Google Scholar]
  25. Y. Reshetnyak, Weak convergence of completely additive vector functions on a set. Sibirski Mat. Zh. 9 (1968) 1386–1394. [Google Scholar]
  26. R.T. Rockafellar, Convex analysis. Princeton Mathematical Series. Princeton University Press, Princeton, NJ (1970). [Google Scholar]
  27. R. Schneider, Convex Bodies: the Brunn-Minkowski Theory. Encyclopedia of Mathematics and its Applications. Cambridge Univeristy Press (1993). [CrossRef] [Google Scholar]
  28. G. Bellettini, V. Caselles and M. Novaga, Explicit solutions of the eigenvalue problem – div (du/|du|) = u in R2. SIAM J. Math. Anal. 36 (2005) 1095–1129. [CrossRef] [Google Scholar]
  29. M. Ghomi, The problem of optimal smoothing for convex functions. Proc. Amer. Math. Soc. 130 (2002) 2255–2259. [CrossRef] [MathSciNet] [Google Scholar]
  30. G. Anzellotti, The Euler equation for functionals with linear growth. Trans. Amer. Math. Soc. 290 (1985) 483–501. [CrossRef] [MathSciNet] [Google Scholar]
  31. H. Brézis, Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert. North-Holland Publishing Co., Amsterdam (1973). (50). [Google Scholar]
  32. F. Andreu-Vaillo, V. Caselles and J.M. Mazón, Parabolic quasilinear equations minimizing linear growth functionals. Vol. 223 of Progress in Mathematics. Birkhäuser Verlag, Basel (2004). [Google Scholar]
  33. S. Moll and F. Smarrazzo, The Neumann problem for one-dimensional parabolic equations with linear growth Lagrangian: evolution of singularities. J. Evol. Equ. 22 (2022). [CrossRef] [Google Scholar]

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