Hertrich, Johannes; Gräf, Manuel; Beinert, Robert; Steidl, Gabriele Wasserstein steepest descent flows of discrepancies with Riesz kernels. (English) Zbl 1540.49049 J. Math. Anal. Appl. 531, No. 1, Part 1, Article ID 127829, 43 p. (2024). Reviewer: Manfred Tasche (Rostock) MSC: 49Q20 65D18 31B15 35A15 46E27 49N90 94A08 49Q22 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Kopfer, Eva; Streets, Jeffrey Optimal transport and generalized Ricci flow. (English) Zbl 1539.53112 SIGMA, Symmetry Integrability Geom. Methods Appl. 20, Paper 003, 15 p. (2024). Reviewer: Wojciech Górny (Wien) MSC: 53E20 49Q22 58J35 × Cite Format Result Cite Review PDF Full Text: arXiv Link
Nüsken, Nikolas; Renger, D. R. Michiel Stein variational gradient descent: many-particle and long-time asymptotics. (English) Zbl 07805177 Found. Data Sci. 5, No. 3, 286-320 (2023). MSC: 62-08 62F15 65F55 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Liero, Matthias; Mielke, Alexander; Savaré, Giuseppe Fine properties of geodesics and geodesic \(\lambda\)-convexity for the Hellinger-Kantorovich distance. (English) Zbl 1533.53035 Arch. Ration. Mech. Anal. 247, No. 6, Paper No. 112, 73 p. (2023). Reviewer: Vyacheslav I. Maksimov (Yekaterinburg) MSC: 53C22 49Q22 × Cite Format Result Cite Review PDF Full Text: DOI arXiv OA License
Li, Bowen; Lu, Jianfeng Interpolation between modified logarithmic Sobolev and Poincaré inequalities for quantum Markovian dynamics. (English) Zbl 1537.46051 J. Stat. Phys. 190, No. 10, Paper No. 161, 70 p. (2023). MSC: 46L53 81P45 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Monsaingeon, Léonard; Tamanini, Luca; Vorotnikov, Dmitry The dynamical Schrödinger problem in abstract metric spaces. (English) Zbl 1516.49013 Adv. Math. 426, Article ID 109100, 55 p. (2023). Reviewer: Alain Brillard (Riedisheim) MSC: 49J45 49Q20 58B20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv OA License
Nhan-Phu Chung; Quoc-Hung Nguyen Gradient flows of modified Wasserstein distances and porous medium equations with nonlocal pressure. (English) Zbl 1514.35007 Acta Math. Vietnam. 48, No. 1, 209-235 (2023). MSC: 35A15 35A01 35A35 35R11 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
De Ponti, Nicolò; Muratori, Matteo; Orrieri, Carlo Wasserstein stability of porous medium-type equations on manifolds with Ricci curvature bounded below. (English) Zbl 1496.35054 J. Funct. Anal. 283, No. 9, Article ID 109661, 58 p. (2022). Reviewer: Feng-Yu Wang (Tianjin) MSC: 35B35 35K15 35R01 35K55 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Stefani, Giorgio Generalized Bakry-Émery curvature condition and equivalent entropic inequalities in groups. (English) Zbl 07493867 J. Geom. Anal. 32, No. 4, Paper No. 136, 98 p. (2022). MSC: 47D07 28D20 53C17 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Brenier, Yann A variational interpretation of general relativity in a vacuum in terms of optimal transport. (Une interprétation variationnelle de la relativité générale dans le vide en termes de transport optimal.) (French) Zbl 07468764 C. R., Math., Acad. Sci. Paris 360, 25-33 (2022). Reviewer: Ion Vancea Vancea (Rio de Janeiro) MSC: 49Q22 83C05 × Cite Format Result Cite Review PDF Full Text: DOI OA License
Huo, Xiaokai; Liu, Hailiang; Tzavaras, Athanasios E.; Wang, Shuaikun An energy stable and positivity-preserving scheme for the Maxwell-Stefan diffusion system. (English) Zbl 1511.65083 SIAM J. Numer. Anal. 59, No. 5, 2321-2345 (2021). Reviewer: Bülent Karasözen (Ankara) MSC: 65M06 65N06 65K10 35K55 35Q79 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Luise, Giulia; Savaré, Giuseppe Contraction and regularizing properties of heat flows in metric measure spaces. (English) Zbl 1459.49030 Discrete Contin. Dyn. Syst., Ser. S 14, No. 1, 273-297 (2021). Reviewer: Lakehal Belarbi (Mostaganem) MSC: 49Q20 47D07 30L99 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Lavenant, Hugo Unconditional convergence for discretizations of dynamical optimal transport. (English) Zbl 1456.65046 Math. Comput. 90, No. 328, 739-786 (2021). MSC: 65K10 49M25 49M41 49Q22 35A15 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Fournier, Nicolas; Perthame, Benoît Transport distances for PDEs: the coupling method. (English) Zbl 1459.35037 EMS Surv. Math. Sci. 7, No. 1, 1-31 (2020). MSC: 35B40 35B45 35Q20 35Q49 35Q84 35K55 35R11 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Gentil, Ivan; Léonard, Christian; Ripani, Luigia Dynamical aspects of the generalized Schrödinger problem via Otto calculus – a heuristic point of view. (English) Zbl 1462.37009 Rev. Mat. Iberoam. 36, No. 4, 1071-1112 (2020). MSC: 37A50 53E20 53E10 60J60 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Ambrosio, Luigi; Mondino, Andrea; Savaré, Giuseppe Nonlinear diffusion equations and curvature conditions in metric measure spaces. (English) Zbl 1477.49003 Memoirs of the American Mathematical Society 1270. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-3913-2/pbk; 978-1-4704-5513-2/ebook). v, 121 p. (2019). Reviewer: Dimitris P. Vartziotis (Ioannina) MSC: 49-02 49J52 49Q22 35K55 58J35 35K90 31C25 58B20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link
Brenier, Yann Geometric origin and some properties of the arctangential heat equation. (English) Zbl 1410.35081 Tunis. J. Math. 1, No. 4, 561-584 (2019). Reviewer: Stepan Agop Tersian (Rousse) MSC: 35L65 53C44 35K55 × Cite Format Result Cite Review PDF Full Text: DOI Link
Brenier, Yann The initial value problem for the Euler equations of incompressible fluids viewed as a concave maximization problem. (English) Zbl 1410.35102 Commun. Math. Phys. 364, No. 2, 579-605 (2018). Reviewer: Vladimir Mityushev (Kraków) MSC: 35Q31 35B65 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Matthes, Daniel; Zinsl, Jonathan Existence of solutions for a class of fourth order cross-diffusion systems of gradient flow type. (English) Zbl 1371.35146 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 159, 316-338 (2017). MSC: 35K46 35D30 49J40 35K65 35A15 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Carlen, Eric A.; Maas, Jan Gradient flow and entropy inequalities for quantum Markov semigroups with detailed balance. (English) Zbl 1386.46057 J. Funct. Anal. 273, No. 5, 1810-1869 (2017). Reviewer: Rolf Gohm (Aberystwyth) MSC: 46L57 81S22 34D05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Carfora, Mauro The Wasserstein geometry of nonlinear \(\sigma\) models and the Hamilton-Perelman Ricci flow. (English) Zbl 1360.53067 Rev. Math. Phys. 29, No. 1, Article ID 1750001, 71 p. (2017). Reviewer: Nicolai K. Smolentsev (Kemerovo) MSC: 53C44 58D25 58D30 81T17 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Shao, Yuanzhen Continuous maximal regularity on singular manifolds and its applications. (English) Zbl 1348.53048 Evol. Equ. Control Theory 5, No. 2, 303-335 (2016). MSC: 53C21 53C44 58J99 35K55 35K65 35K67 35R01 74K15 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Kell, Martin \(q\)-heat flow and the gradient flow of the Renyi entropy in the \(p\)-Wasserstein space. (English) Zbl 1375.53056 J. Funct. Anal. 271, No. 8, 2045-2089 (2016). Reviewer: Przemysław Górka (Warsaw) MSC: 53C23 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Liero, Matthias; Mielke, Alexander; Savaré, Giuseppe Optimal transport in competition with reaction: the Hellinger-Kantorovich distance and geodesic curves. (English) Zbl 1347.49078 SIAM J. Math. Anal. 48, No. 4, 2869-2911 (2016). MSC: 49Q20 49K21 58E30 35K57 28A33 46E27 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Bogachev, V. I.; Röckner, M.; Shaposhnikov, S. V. Distances between transition probabilities of diffusions and applications to nonlinear Fokker-Planck-Kolmogorov equations. (English) Zbl 1345.35051 J. Funct. Anal. 271, No. 5, 1262-1300 (2016). Reviewer: Stefanie Sonner (Graz) MSC: 35K15 60J60 35Q84 35K55 × Cite Format Result Cite Review PDF Full Text: DOI
Esselborn, Elias; Gigli, Nicola; Otto, Felix Algebraic contraction rate for distance between entropy solutions of scalar conservation laws. (English) Zbl 1332.35216 J. Math. Anal. Appl. 435, No. 2, 1525-1551 (2016). MSC: 35L65 35B35 × Cite Format Result Cite Review PDF Full Text: DOI
Zinsl, Jonathan; Matthes, Daniel Transport distances and geodesic convexity for systems of degenerate diffusion equations. (English) Zbl 1342.49067 Calc. Var. Partial Differ. Equ. 54, No. 4, 3397-3438 (2015). MSC: 49Q20 49K20 49J40 35K40 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Wu, Lijiang; Slepčev, Dejan Nonlocal interaction equations in environments with heterogeneities and boundaries. (English) Zbl 1327.35057 Commun. Partial Differ. Equations 40, No. 7, 1241-1281 (2015). MSC: 35D30 45K05 49K20 92D50 × Cite Format Result Cite Review PDF Full Text: DOI Link
Erbar, Matthias; Kuwada, Kazumasa; Sturm, Karl-Theodor On the equivalence of the entropic curvature-dimension condition and Bochner’s inequality on metric measure spaces. (English) Zbl 1329.53059 Invent. Math. 201, No. 3, 993-1071 (2015). MSC: 53C23 58J65 28A33 53C20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Erbar, Matthias; Huesmann, Martin Curvature bounds for configuration spaces. (English) Zbl 1335.53047 Calc. Var. Partial Differ. Equ. 54, No. 1, 397-430 (2015). Reviewer: Ahmad Afuni (Bremen) MSC: 53C21 28A33 58C35 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Gentil, Ivan Dimensional contraction in Wasserstein distance for diffusion semigroups on a Riemannian manifold. (English) Zbl 1390.58021 Potential Anal. 42, No. 4, 861-873 (2015). Reviewer: Maria Gordina (Storrs) MSC: 58J65 58J35 53B21 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Ambrosio, Luigi; Gigli, Nicola; Savaré, Giuseppe Bakry-Émery curvature-dimension condition and Riemannian Ricci curvature bounds. (English) Zbl 1307.49044 Ann. Probab. 43, No. 1, 339-404 (2015). Reviewer: Vasile Oproiu (Iaşi) MSC: 49Q20 47D07 30L99 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid
Carlen, Eric A.; Maas, Jan An analog of the 2-Wasserstein metric in non-commutative probability under which the fermionic Fokker-Planck equation is gradient flow for the entropy. (English) Zbl 1297.35241 Commun. Math. Phys. 331, No. 3, 887-926 (2014). MSC: 35Q84 46L53 53C22 81R15 82C31 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Bolley, François; Gentil, Ivan; Guillin, Arnaud Dimensional contraction via Markov transportation distance. (English) Zbl 1312.47055 J. Lond. Math. Soc., II. Ser. 90, No. 1, 309-332 (2014). Reviewer: Gong Guanglu (Beijing) MSC: 47D07 60J25 60J60 × Cite Format Result Cite Review PDF Full Text: DOI arXiv HAL
Giacomin, Giambattista; Luçon, Eric; Poquet, Christophe Coherence stability and effect of random natural frequencies in populations of coupled oscillators. (English) Zbl 1296.35194 J. Dyn. Differ. Equations 26, No. 2, 333-367 (2014). Reviewer: Alain Brillard (Riedisheim) MSC: 35Q84 37N25 82C31 60J65 35B35 47D06 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Di Francesco, Marco; Matthes, Daniel Curves of steepest descent are entropy solutions for a class of degenerate convection-diffusion equations. (English) Zbl 1293.35149 Calc. Var. Partial Differ. Equ. 50, No. 1-2, 199-230 (2014). MSC: 35K65 35A02 35L65 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Gigli, Nicola; Mantegazza, Carlo A flow tangent to the Ricci flow via heat kernels and mass transport. (English) Zbl 1288.53059 Adv. Math. 250, 74-104 (2014). MSC: 53C44 58C35 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Seis, Christian Long-time asymptotics for the porous medium equation: the spectrum of the linearized operator. (English) Zbl 1293.35254 J. Differ. Equations 256, No. 3, 1191-1223 (2014). Reviewer: Valery V. Karachik (Chelyabinsk) MSC: 35Q35 35B40 35P10 35J60 76S05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Liero, Matthias; Mielke, Alexander Gradient structures and geodesic convexity for reaction-diffusion systems. (English) Zbl 1292.35149 Philos. Trans. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 371, No. 2005, 20120346, 28 p. (2013). MSC: 35K57 35K51 35K59 × Cite Format Result Cite Review PDF Full Text: DOI
Mielke, Alexander Geodesic convexity of the relative entropy in reversible Markov chains. (English) Zbl 1282.60072 Calc. Var. Partial Differ. Equ. 48, No. 1-2, 1-31 (2013). Reviewer: Piotr Garbaczewski (Opole) MSC: 60J27 53C21 53C23 82C41 82C31 × Cite Format Result Cite Review PDF Full Text: DOI
König, Wolfgang (ed.); Mörters, Peter (ed.); Peletier, Mark (ed.); Zimmer, Johannes (ed.) Interplay of analysis and probability in physics. Abstracts from the workshop held January 22–28, 2012. (English) Zbl 1349.00213 Oberwolfach Rep. 9, No. 1, 281-349 (2012). MSC: 00B05 00B25 82-06 60-06 × Cite Format Result Cite Review PDF Full Text: DOI
Gigli, Nicola Optimal maps in non branching spaces with Ricci curvature bounded from below. (English) Zbl 1257.53055 Geom. Funct. Anal. 22, No. 4, 990-999 (2012). Reviewer: Dumitru Motreanu (Perpignan) MSC: 53C20 49J15 28C15 × Cite Format Result Cite Review PDF Full Text: DOI
Erbar, Matthias; Maas, Jan Ricci curvature of finite Markov chains via convexity of the entropy. (English) Zbl 1256.53028 Arch. Ration. Mech. Anal. 206, No. 3, 997-1038 (2012). MSC: 53C20 28C15 58C35 60J10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Chow, Shui-Nee; Huang, Wen; Li, Yao; Zhou, Haomin Fokker-Planck equations for a free energy functional or Markov process on a graph. (English) Zbl 1256.35173 Arch. Ration. Mech. Anal. 203, No. 3, 969-1008 (2012). MSC: 35Q84 60H15 35Q60 × Cite Format Result Cite Review PDF Full Text: DOI
Lisini, Stefano; Matthes, Daniel; Savaré, Giuseppe Cahn-Hilliard and thin film equations with nonlinear mobility as gradient flows in weighted-Wasserstein metrics. (English) Zbl 1248.35095 J. Differ. Equations 253, No. 2, 814-850 (2012). MSC: 35K35 35K59 35B09 35D30 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Natile, Luca; Peletier, Mark A.; Savaré, Giuseppe Contraction of general transportation costs along solutions to Fokker-Planck equations with monotone drifts. (English) Zbl 1206.35236 J. Math. Pures Appl. (9) 95, No. 1, 18-35 (2011). MSC: 35Q84 35K10 60J60 82C31 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Carrillo, J. A.; Lisini, S.; Savaré, G.; Slepčev, D. Nonlinear mobility continuity equations and generalized displacement convexity. (English) Zbl 1225.49043 J. Funct. Anal. 258, No. 4, 1273-1309 (2010). MSC: 49Q20 49J40 35K55 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Carrillo, José A.; Slepčev, Dejan Example of a displacement convex functional of first order. (English) Zbl 1180.35293 Calc. Var. Partial Differ. Equ. 36, No. 4, 547-564 (2009). MSC: 35K58 35K35 × Cite Format Result Cite Review PDF Full Text: DOI
Lott, John Optimal transport and Perelman’s reduced volume. (English) Zbl 1171.53318 Calc. Var. Partial Differ. Equ. 36, No. 1, 49-84 (2009). MSC: 53C21 53C44 49J20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Dolbeault, Jean; Nazaret, Bruno; Savaré, Giuseppe A new class of transport distances between measures. (English) Zbl 1157.49042 Calc. Var. Partial Differ. Equ. 34, No. 2, 193-231 (2009). MSC: 49Q20 49J40 47J30 × Cite Format Result Cite Review PDF Full Text: DOI arXiv HAL
Michel, Philippe A singular asymptotic behavior of a transport equation. (English) Zbl 1134.35008 C. R., Math., Acad. Sci. Paris 346, No. 3-4, 155-159 (2008). MSC: 35A20 82C70 × Cite Format Result Cite Review PDF Full Text: DOI HAL
Lisini, Stefano Characterization of absolutely continuous curves in Wasserstein spaces. (English) Zbl 1132.60004 Calc. Var. Partial Differ. Equ. 28, No. 1, 85-120 (2007). Reviewer: Alessandro Duci (Bergamo) MSC: 60B05 49J55 × Cite Format Result Cite Review PDF Full Text: DOI
Carrillo, José A.; Di Francesco, Marco; Toscani, Giuseppe Intermediate asymptotics beyond homogeneity and self-similarity: long time behavior for \(u_t = \Delta\varphi(u)\). (English) Zbl 1096.35015 Arch. Ration. Mech. Anal. 180, No. 1, 127-149 (2006). Reviewer: Messoud A. Efendiev (Berlin) MSC: 35B40 35K65 35K15 × Cite Format Result Cite Review PDF Full Text: DOI