Free Access
Volume 25, 2019
Article Number 42
Number of page(s) 21
Published online 20 September 2019
  1. L. Ambrosio, N. Gigli and G. Savaré, Gradient Flows: In Metric Spaces and in the Space of Probability Measures. Springer Science & Business Media, Basel (2008). [Google Scholar]
  2. G. Anzellotti, Pairing between measures and bounded functions and compensated compactness. Ann. Mat. Pura Appl. IV 135 (1983) 293–318. [CrossRef] [MathSciNet] [Google Scholar]
  3. G. Bellettini, V. Caselles and M. Novaga, The total variation flow in ℝn. J. Differ. Equ. 184 (2002) 475–525. [Google Scholar]
  4. M. Benning, L. Calatroni, B. Düring and C.-B. Schönlieb, A primal-dual approach for a total variation Wasserstein flow. Geometric Science of Information, Springer, Heidelberg (2013) 413–421. [CrossRef] [Google Scholar]
  5. Y. Brenier, Polar factorization and monotone rearrangement of vector-valued functions. Commun. Pure Appl. Math. 44 (1991) 375–417. [Google Scholar]
  6. H. Brezis, Analyse fonctionnelle. Théorie et applications [Theory and applications]. Collection Mathématiques Appliquées pour la Maîtrise [Collection of Applied Mathematics for the Master’s Degree]. Masson, Paris (1983). [Google Scholar]
  7. M. Burger, M. Franek and C.-B. Schönlieb, Regularized regression and density estimation based on optimal transport. Appl. Math. Res. Express 2012 (2012) 209–253. [Google Scholar]
  8. G. Carlier and M. Laborde, A splitting method for nonlinear diffusions with nonlocal, nonpotential drifts. Nonlinear Anal. 150 (2017) 1–18. [CrossRef] [Google Scholar]
  9. A. Chambolle, V. Caselles, D. Cremers, M. Novaga and T. Pock, An introduction to total variation for image analysis, in Theoretical Foundations and Numerical Methods for Sparse Recovery. Vol. 9 of Radon Ser. Comput. Appl. Math. Walter de Gruyter, Berlin (2010) 263–340. [Google Scholar]
  10. A. Chambolle, V. Duval, G. Peyré and C. Poon, Geometric properties of solutions to the total variation denoising problem. Inverse Probl. 33 (2016) 015002. [Google Scholar]
  11. G. De Philippis, A.R. Mészáros, F. Santambrogio and B. Velichkov, BV estimates in optimal transportation and applications. Arch. Ration. Mech. Anal. 219 (2016) 829–860. [Google Scholar]
  12. M. Di Francesco and D. Matthes, Curves of steepest descent are entropy solutions for a class of degenerate convection-diffusion equations. Calc. Var. Partial Differ. Equ. 50 (2014) 199–230. [Google Scholar]
  13. B. Düring and C.-B. Schönlieb, A high-contrast fourth-order pde from imaging: numerical solution by ADI splitting, in Multi-scale and High-Contrast Partial Differential Equations, edited by H. Ammari, et al. (2012) 93–103. [Google Scholar]
  14. L.C. Evans and J. Spruck, Motion of level sets by mean curvature. II Trans. Amer. Math. Soc. 330 (1992) 321–332 [CrossRef] [Google Scholar]
  15. M.-H. Giga and Y. Giga, Very singular diffusion equations: second and fourth order problems. Jpn. J. Ind. Appl. Math. 27 (2010) 323–345. [Google Scholar]
  16. Y. Giga, H. Kuroda and H. Matsuoka, Fourth-order total variation flow with Dirichlet condition: characterization of evolution and extinction time estimates. Adv. Math. Sci. Appl. 24 (2014) 499–534. [Google Scholar]
  17. R. Jordan, D. Kinderlehrer and F. Otto, The variational formulation of the Fokker–Planck equation. SIAM J. Math. Anal. 29 (1998) 1–17. [CrossRef] [MathSciNet] [Google Scholar]
  18. D. Loibl, D. Matthes and J. Zinsl, Existence of weak solutions to a class of fourth order partial differential equations with Wasserstein gradient structure. Potential Anal. 45 (2016) 755–776. [CrossRef] [Google Scholar]
  19. U. Massari, Esistenza e regolarita delle ipersuperfici di curvatura media assegnata in ℝn. Arch. Ration. Mech. Anal. 55 (1974) 357–382. [Google Scholar]
  20. U. Massari, Frontiere orientate di curvatura media assegnata in Lp. Rend. Sem. Mat. Univ. Padova 53 (1975) 37–52. [Google Scholar]
  21. E.G.-U. Massari, Variational mean curvatures. Rend. Sem. Mat. Univ. Pol. Torino 52 (1994) 1–28. [Google Scholar]
  22. D. Matthes, R.J. McCann and Giuseppe Savaré, A family of nonlinear fourth order equations of gradient flow type. Commun. Partial Differ. Equ. 34 (2009) 1352–1397. [CrossRef] [Google Scholar]
  23. R.J. McCann, A convexity principle for interacting gases. Adv. Math. 128 (1997) 153–179. [CrossRef] [MathSciNet] [Google Scholar]
  24. R. Rossi and G. Savaré, Tightness, integral equicontinuity and compactness for evolution problems in Banach spaces. Ann. Scu. Norm. Super. Pisa-Cl. Sci. 2 (2003) 395–431. [Google Scholar]
  25. L.I. Rudin, S. Osher and E. Fatemi, Nonlinear total variation based noise removal algorithms. In Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental Mathematics: Computational Issues in Nonlinear Science. Los Alamos, NM (1991). Physics D 60 (1992) 259–268. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  26. F. Santambrogio, Optimal Transport for Applied Mathematicians. Calculus of variations, PDEs, and modeling. Vol. 87 of Progress in Nonlinear Differential Equations and their Applications. Birkhäuser/Springer, Cham (2015). [CrossRef] [Google Scholar]
  27. I. Tamanini, Boundaries of Caccioppoli sets with Hölder-continuous normal vector. J. für Die Reineund Angewandte Mathematik 334 (1982) 27–39. [Google Scholar]
  28. C. Villani, Topics in Optimal Transportation. Vol. 58 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI (2003). [CrossRef] [Google Scholar]

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