Free Access
Volume 27, 2021
Article Number 18
Number of page(s) 29
Published online 22 March 2021
  1. F. Almgren, J.E. Taylor and L. Wang, Curvature-driven flows: a variational approach. SIAM J. Control Optim. 31 (1993) 387–438. [Google Scholar]
  2. L. Ambrosio, N. Gigli and G. Savaré, Gradient Flows in Metric Spaces and in the Space of Probability Measures. Lectures in mathematics. ETH Zürich, Birkhäuser (2005). [Google Scholar]
  3. A. Braides, Local Minimization, Variational Evolution and Γ-Convergence. Vol. 2094 of Lecture Notes in Mathematics. Springer (2012). [Google Scholar]
  4. L. Chizat and S. Di Marino A tumor growth model of Hele-Shaw type as a gradient flow. ESAIM: COCV 26 (2020) 103. [EDP Sciences] [Google Scholar]
  5. L. Chizat, G. Peyré, B. Schmitzer and F.-X. Vialard, An interpolating distance between optimal transport and Fisher–Rao metrics. Found. Comput. Math. 18 (2018) 1–44. [CrossRef] [Google Scholar]
  6. L. Chizat, G. Peyré, B. Schmitzer and F.-X. Vialard, Unbalanced optimal transport: dynamic and Kantorovich formulations. J. Funct.Anal. 274 (2018) 3090–3123. [Google Scholar]
  7. E. De Giorgi, New problems on minimizing movements, in Boundary Value Problems for PDE and Applications, edited by C. Baiocchi and J.L. Lions. Masson (1993) 81–98. [Google Scholar]
  8. E. De Giorgi, A. Marino and M. Tosques, Problems of evolution in metric spaces and maximal decreasing curve. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 68 (1980) 180–187. [Google Scholar]
  9. M. Degiovanni, A. Marino and M. Tosques, Evolution equations with lack of convexity. Nonlinear Anal. 9 (1985) 1401–1443. [CrossRef] [MathSciNet] [Google Scholar]
  10. F. Fleißner, Gamma-convergence and relaxations for gradient flows in metric spaces: a minimizing movement approach. ESAIM: COCV 25 (2019) 28. [EDP Sciences] [Google Scholar]
  11. F. Fleißner, A note on the differentiability of the Hellinger-Kantorovich distances. Preprint arXiv:2007.07225 (2020). [Google Scholar]
  12. F. Fleißner and G. Savaré, Reverse approximation of gradient flows as minimizing movements: a conjecture by De Giorgi. Annali della Scuola Normale di Pisa - Classe di Scienze 20 (2020) 677–720. [Google Scholar]
  13. I. Fonseca and G. Leoni, Modern Methods in the Calculus of Variations: Lp Spaces. Springer Science & Business Media (2007). [Google Scholar]
  14. T.O. Gallouët and L. Monsaingeon, A JKO splitting scheme for Kantorovich–Fisher–Rao gradient flows. SIAM J. Math. Anal. 49 (2017) 1100–1130. [CrossRef] [Google Scholar]
  15. W. Gangbo and R.J. McCann, The geometry of optimal transportation. Acta Math. 177 (1996) 113–161. [Google Scholar]
  16. R. Jordan, D. Kinderlehrer and F. Otto, Free energy and the Fokker-Planck equation. Physica D 107 (1997) 265–271. [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. [Google Scholar]
  18. S. Kondratyev, L. Monsaingeon and D. Vorotnikov, A fitness-driven cross-diffusion system from population dynamics as a gradient flow. J. Differ. Equ. 261 (2016) 2784–2808. [Google Scholar]
  19. S. Kondratyev, L. Monsaingeon and D. Vorotnikov, et al., A new optimal transport distance on the space of finite Radon measures. Adv. Differ. Equ. 21 (2016) 1117–1164. [Google Scholar]
  20. S. Kondratyev and D. Vorotnikov, Nonlinear Fokker-Planck equations with reaction as gradient flows of the free energy. J. Funct. Anal. 278 (2020) 108310. [Google Scholar]
  21. M. Liero, A. Mielke and G. Savaré, On geodesic λ-convexity with respect to the Hellinger-Kantorovich distance, in preparation. [Google Scholar]
  22. M. Liero, A. Mielke and G. Savaré, Optimal transport in competition with reaction: the Hellinger–Kantorovich distance and geodesic curves. SIAM J. Math. Anal. 48 (2016) 2869–2911. [CrossRef] [Google Scholar]
  23. M. Liero, A. Mielke and G. Savaré, Optimal entropy-transport problems and a new Hellinger–Kantorovich distance between positive measures. Invent. Math. 211 (2018) 969–1117. [Google Scholar]
  24. A. Marino, C. Saccon and M. Tosques, Curves of maximal slope and parabolic variational inequalities on nonconvex constraints. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 16 (1989) 281–330. [Google Scholar]
  25. A. Mielke, Differential, energetic, and metric formulations for rate-independent processes. Springer (2011). [Google Scholar]
  26. A. Mielke, A gradient structure for reaction–diffusion systems and for energy-drift-diffusion systems. Nonlinearity 24 (2011) 1329. [Google Scholar]
  27. A. Mielke and F. Rindler, Reverse approximation of energetic solutions to rate-independent processes. NoDEA Nonlinear Differ. Equ. Appl. 16 (2009) 17–40. [Google Scholar]
  28. A. Mielke, R. Rossi and G. Savaré, Balanced viscosity (BV) solutions to infinite-dimensional rate-independent systems. J. Eur. Math. Soc. 18 (2016) 2107–2165. [CrossRef] [Google Scholar]
  29. F. Otto, The geometry of dissipative evolution equations: the porous medium equation. Commun. Partial Differ. Equ. 26 (2001) 101–174. [Google Scholar]
  30. C. Villani, Topics in optimal transportation. Vol. 58 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI (2003). [CrossRef] [Google Scholar]
  31. C. Villani, Optimal transport. Old and new. Vol. 338 of Grundlehren der Mathematischen Wissenschaften. Springer-Verlag, Berlin (2009). [CrossRef] [Google Scholar]

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