Preprints, accepted papers, published papers, books, contributions to volumes or proceedings, edited books.


Preprints

  1. Luca Minotti, Giuseppe Savaré
    Viscous corrections of the Time Incremental Minimization Scheme and Visco-Energetic Solutions to Rate-Independent Evolution Problems
    ArXiv e-prints 1606.03359 (2016) 1-60
    arxiv:1606.03359
  2. Alexander Mielke, Riccarda Rossi, Giuseppe Savaré
    Global existence results for viscoplasticity at finite strain
    ArXiv e-prints 1609.08832 (2016) 1-48
    arxiv:1609.08832
  3. Matthias Liero, Alexander Mielke, Giuseppe Savaré
    Optimal Entropy-Transport problems and a new Hellinger-Kantorovich distance between positive measures
    ArXiv e-prints 1508.07941 (2015) 1-103
    arxiv:1508.07941

Accepted papers

  1. Riccarda Rossi, Giuseppe Savaré
    From Visco-Energetic to Energetic and Balanced Viscosity solutions of rate-independent systems
    ArXiv e-prints 1702.00136 (2017) 1-27
    arxiv:1702.00136
  2. Luigi Ambrosio, Andrea Mondino, Giuseppe Savaré
    Nonlinear diffusion equations and curvature conditions in metric measure spaces
    Memoirs of the A.M.S., in press 1509.07273 (2015) 1-108
    arxiv:1509.07273

Published papers

  1. Ambrosio Luigi, Erbar Matthias, Savaré Giuseppe
    Optimal transport, Cheeger energies and contractivity of dynamic transport distances in extended spaces.
    Nonlinear Anal. 137 (2016) 77--134
    doi:10.1016/j.na.2015.12.006
    arxiv:1506.05932
  2. Ambrosio Luigi, Mondino Andrea, Savaré Giuseppe
    On the Bakry-Émery condition, the gradient estimates and the local-to-global property of RCD^*(K,N) metric measure spaces.
    J. Geom. Anal. 26 (2016) 24--56
    doi:10.1007/s12220-014-9537-7
    arxiv:1309.4664
  3. Mielke Alexander, Rossi Riccarda, Savaré Giuseppe
    Balanced-viscosity solutions for multi-rate systems.
    J. Phys. Conf. Ser. 727 (2016) 012010, 26
    doi:10.1088/1742-6596/727/1/012010
    arxiv:1409.0955
  4. Liero Matthias, Mielke Alexander, Savaré Giuseppe
    Optimal Transport in Competition with Reaction: The Hellinger--Kantorovich Distance and Geodesic Curves.
    SIAM J. Math. Anal. 48 (2016) 2869--2911
    doi:10.1137/15M1041420
    arxiv:1509.00068
  5. Mielke Alexander, Rossi Riccarda, Savaré Giuseppe
    Balanced viscosity (BV) solutions to infinite-dimensional rate-independent systems.
    J. Eur. Math. Soc. (JEMS) 18 (2016) 2107--2165
    doi:10.4171/JEMS/639
    arxiv:1309.6291
  6. Ambrosio Luigi, Gigli Nicola, Savaré Giuseppe
    Bakry-Émery curvature-dimension condition and Riemannian Ricci curvature bounds.
    Ann. Probab. 43 (2015) 339--404
    doi:10.1214/14-AOP907
    arxiv:1209.5786
  7. Luigi Ambrosio, Simone Di Marino, Giuseppe Savaré
    On the duality between p-modulus and probability measures.
    J. Eur. Math. Soc. (JEMS) 17 (2015) 1817--1853
    doi:10.4171/JEMS/546
    arxiv:1311.1381
  8. Gigli Nicola, Mondino Andrea, Savaré Giuseppe
    Convergence of pointed non-compact metric measure spaces and stability of Ricci curvature bounds and heat flows.
    Proc. Lond. Math. Soc. (3) 111 (2015) 1071--1129
    doi:10.1112/plms/pdv047
    arxiv:1311.4907
  9. Agostiniani Virginia, Rossi Riccarda, Savaré Giuseppe
    On the transversality conditions and their genericity.
    Rend. Circ. Mat. Palermo (2) 64 (2015) 101--116
    doi:10.1007/s12215-014-0184-4
    arxiv:1310.4846
  10. Luigi Ambrosio, Nicola Gigli, Giuseppe Savaré
    Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below.
    Invent. Math. 195 (2014) 289--391
    doi:10.1007/s00222-013-0456-1
    arxiv:1106.2090
    http://rdcu.be/mE8H (View-only version)
  11. Ambrosio Luigi, Gigli Nicola, Savaré Giuseppe
    Metric measure spaces with Riemannian Ricci curvature bounded from below.
    Duke Math. J. 163 (2014) 1405--1490
    doi:10.1215/00127094-2681605
    arxiv:1109.0222
  12. Giuseppe Savaré
    Self-improvement of the Bakry-Émery condition and Wasserstein contraction of the heat flow in RCD(K,\infty) metric measure spaces.
    Disc. Cont. Dyn. Sist. A 34 (2014) 1641-1661
    doi:10.3934/dcds.2014.34.1641
    arxiv:1304.0643
  13. Savaré Giuseppe, Toscani Giuseppe
    The concavity of Rényi entropy power.
    IEEE Trans. Inform. Theory 60 (2014) 2687--2693
    doi:10.1109/TIT.2014.2309341
    arxiv:1208.1035
  14. Brenier Y., Gangbo W., Savaré G., Westdickenberg M.
    Sticky particle dynamics with interactions.
    J. Math. Pures Appl. (9) 99 (2013) 577--617
    doi:10.1016/j.matpur.2012.09.013
    arxiv:1201.2350v1
  15. Riccarda Rossi, Giuseppe Savaré
    A characterization of Energetic and BV solutions to one-dimensional rate-independent systems.
    Discrete Contin. Dyn. Syst. (S) 6 (2013) 167-191
    doi:10.3934/dcdss.2013.6.167
  16. Alexander Mielke, Riccarda Rossi, Giuseppe Savaré
    Nonsmooth analysis of doubly nonlinear evolution equations.
    Calc. Var. Partial Differential Equations 46 (2013) 253-310
    doi:10.1007/s00526-011-0482-z
    arxiv:1105.4296
    http://rdcu.be/mE8J (View-only version)
  17. Luigi Ambrosio, Nicola Gigli, Giuseppe Savaré
    Density of Lipschitz functions and equivalence of weak gradients in metric measure spaces.
    Rev. Mat. Iberoamericana 29 (2013) 969-986`
    doi:10.4171/RMI/746
    arxiv:1111.3730
  18. Alexander Mielke, Riccarda Rossi, Giuseppe Savaré
    BV solutions and viscosity approximations of rate-independent systems.
    ESAIM: Control, Optimisation and Calculus of Variations 8 (2012) 36-80
    doi:10.1051/cocv:2006013
    arxiv:0910.3360v1
  19. Simona Fornaro, Stefano Lisini, Giuseppe Savaré, Giuseppe Toscani
    Measure valued solutions of sub-linear diffusion equations with a drift term.
    Discrete Contin. Dyn. Syst. (A) 32 (2012) 1675 - 1707
    doi:10.3934/dcds.2012.32.1675
    arxiv:1009.4305v1
  20. Steffen Arnrich, Alexander Mielke, Mark A. Peletier, Giuseppe Savaré, Marco Veneroni
    Passing to the Limit in a Wasserstein Gradient Flow: From Diffusion to Reaction.
    Calc. Var. Partial Differential Equations 44 (2012) 419--454
    doi:10.1007/s00526-011-0440-9
    arxiv:1102.1202v1
    http://rdcu.be/mE8S (View-only version)
  21. Mark A. Peletier, Giuseppe Savaré, Marco Veneroni
    Chemical Reactions as \Gamma-Limit of Diffusion.
    SIAM Review 54 (2012) 327--352
    doi:10.1137/110858781
  22. Stefano Lisini, Daniel Matthes, Giuseppe Savaré
    Cahn-Hilliard and Thin Film equations with nonlinear mobility as gradient flows in weighted-Wasserstein metrics.
    J. Differential Equations 253 (2012) 814-850
    doi:10.1016/j.jde.2012.04.004
    arxiv:1201.2367
  23. Dolbeault Jean, Nazaret Bruno, Savaré Giuseppe
    From Poincaré to logarithmic Sobolev inequalities: a gradient flow approach.
    SIAM J. Math. Anal. 44 (2012) 3186--3216
    doi:10.1137/110835190
    arxiv:1105.4511
  24. Mielke Alexander, Rossi Riccarda, Savaré Giuseppe
    Variational convergence of gradient flows and rate-independent evolutions in metric spaces.
    Milan J. Math. 80 (2012) 381--410
    doi:10.1007/s00032-012-0190-y
    http://rdcu.be/mE8W (View-only version)
  25. Luca Natile, Mark A. Peletier, Giuseppe Savaré
    Contraction of general transportation costs along solutions to Fokker-Planck equations with monotone drifts.
    Journal de Mathématiques Pures et Appliqués 95 (2011) 18--35
    doi:10.1016/j.matpur.2010.07.003
  26. Rossi Riccarda, Savaré Giuseppe, Segatti Antonio, Stefanelli Ulisse
    A variational principle for gradient flows in metric spaces.
    C. R. Math. Acad. Sci. Paris 349 (2011) 1225--1228
    doi:10.1016/j.crma.2011.11.002
  27. Josè A. Carrillo, Stefano Lisini, Giuseppe Savaré, Dejan Slepcev
    Nonlinear mobility continuity equations and generalized displacement convexity.
    J. Funct. Anal. 258 (2010) 1273--1309
    doi:10.1016/j.jfa.2009.10.016
    arxiv:0901.3978v1
  28. Mark A. Peletier, Giuseppe Savaré, Marco Veneroni
    From diffusion to reaction via \Gamma-convergence.
    SIAM J. Math. Anal. 42 (2010) 1805--1825
    doi:10.1137/090781474
    arxiv:0912.5077v1
  29. Daniel Matthes, Robert J. McCann, Giuseppe Savaré
    A family of nonlinear fourth order equations of gradient flow type.
    Comm. Partial Differential Equations 34 (2009) 1352--1397
    doi:10.1080/03605300903296256
    arxiv:0901.0540v1
  30. Luca Natile, Giuseppe Savaré
    A Wasserstein approach to the one-dimensional sticky particle system.
    SIAM J. Math. Anal. 41 (2009) 1340-1365
    doi:10.1137/090750809
    arxiv:0902.4373v1
  31. Jean Dolbeault, Bruno Nazaret, Giuseppe Savaré
    A new class of transport distances between measures.
    Calc. Var. Partial Differential Equations 34 (2009) 193--231
    doi:10.1007/s00526-008-0182-5
    arxiv:0803.1235v1
    http://rdcu.be/mE83 (View-only version)
  32. Luigi Ambrosio, Giuseppe Savaré, Lorenzo Zambotti
    Existence and stability for Fokker-Planck equations with log-concave reference measure.
    Probab. Theory Related Fields 145 (2009) 517--564
    doi:10.1007/s00440-008-0177-3
    arxiv:0704.2458v1
    http://rdcu.be/mE9a (View-only version)
  33. Ugo Gianazza, Giuseppe Savaré, Giuseppe Toscani
    The Wasserstein gradient flow of the Fisher information and the quantum drift-diffusion equation.
    Arch. Ration. Mech. Anal. 194 (2009) 133--220
    doi:10.1007/s00205-008-0186-5
    http://rdcu.be/mE88 (View-only version)
  34. Alexander Mielke, Riccarda Rossi, Giuseppe Savaré
    Modeling solutions with jumps for rate-independent systems on metric spaces.
    Discrete Contin. Dyn. Syst. 25 (2009) 585--615
    doi:10.3934/dcds.2009.25.585
    arxiv:0807.0744v1
  35. Riccarda Rossi, Alexander Mielke, Giuseppe Savaré
    A metric approach to a class of doubly nonlinear evolution equations and applications.
    Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 7 (2008) 97--169
  36. Sara Daneri, Giuseppe Savaré
    Eulerian calculus for the displacement convexity in the Wasserstein distance.
    SIAM J. Math. Anal. 40 (2008) 1104--1122
    doi:10.1137/08071346X
    arxiv:0801.2455v1
  37. Jean Dolbeault, Bruno Nazaret, Giuseppe Savaré
    On the Bakry-Emery criterion for linear diffusions and weighted porous media equations.
    Commun. Math. Sci. 6 (2008) 477-494
    http://projecteuclid.org/euclid.cms/1214949932
    arxiv:0712.2211v1
  38. Giuseppe Savaré
    Gradient flows and diffusion semigroups in metric spaces under lower curvature bounds.
    C. R. Math. Acad. Sci. Paris 345 (2007) 151--154
    doi:10.1016/j.crma.2007.06.018
  39. Luigi Ambrosio, Stefano Lisini, Giuseppe Savaré
    Stability of flows associated to gradient vector fields and convergence of iterated transport maps.
    Manuscripta Math. 121 (2006) 1--50
    doi:10.1007/s00229-006-0003-0
    http://rdcu.be/mE9g (View-only version)
  40. Micol Pennacchio, Giuseppe Savaré, Piero Colli Franzone
    Multiscale modeling for the bioelectric activity of the heart.
    SIAM J. Math. Anal. 37 (2006) 1333--1370 (electronic)
    doi:10.1137/040615249
  41. Ricardo H. Nochetto, Giuseppe Savaré
    Nonlinear evolution governed by accretive operators in Banach spaces: error control and applications.
    Math. Models Methods Appl. Sci. 16 (2006) 439--477
    doi:10.1142/S0218202506001224
  42. Riccarda Rossi, Giuseppe Savaré
    Gradient flows of non convex functionals in Hilbert spaces and applications.
    ESAIM Control Optim. Calc. Var. 12 (2006) 564--614 (electronic)
  43. Riccarda Rossi, Giuseppe Savaré
    Existence and approximation results for gradient flows.
    Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 15 (2004) 183--196
  44. Luigi Ambrosio, Nicola Gigli, Giuseppe Savaré
    Gradient flows with metric and differentiable structures, and applications to the Wasserstein space.
    Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 15 (2004) 327--343
  45. Riccarda Rossi, Giuseppe Savaré
    Tightness, Integral Equicontinuity and Compactness for Evolution Problems in Banach Spaces.
    Ann. Sc. Norm. Sup., Pisa 2 (2003) 395-431
  46. Piero Colli Franzone, Giuseppe Savaré
    Degenerate Evolution Systems Modeling the Cardiac Electric Field at Micro- and Macroscopic Level.
    50 (2002) 49-78
  47. Giuseppe Savaré
    Compactness properties for families of quasistationary solutions of some evolution equations.
    Trans. Amer. Math. Soc. 354 (2002) 3703--3722
    doi:10.1090/S0002-9947-02-03035-0
  48. Giuseppe Savaré, Giulio Schimperna
    Domain perturbations and estimates for the solutions of second order elliptic equations.
    J. Math. Pures Appl. (9) 81 (2002) 1071--1112
    doi:10.1016/S0021-7824(02)01256-4
  49. Marco Luigi Bernardi, Gianni Arrigo Pozzi, Giuseppe Savaré
    Variational equations of Schroedinger-type in non-cylindrical domains.
    J. Differential Equations 171 (2001) 63--87
    doi:10.1006/jdeq.2000.3834
  50. Nochetto Ricardo H., Savaré Giuseppe, Verdi Claudio
    A posteriori error estimates for variable time-step discretizations of nonlinear evolution equations.
    Comm. Pure Appl. Math. 53 (2000) 525--589
    3.0.CO;2-M>doi:10.1002/(SICI)1097-0312(200005)53:5<525::AID-CPA1>3.0.CO;2-M
  51. Luigi Ambrosio, Piero Colli Franzone, Giuseppe Savaré
    On the asymptotic behaviour of anisotropic energies arising in the Cardiac Bidomain model.
    Interfaces Free Bound. 2 (2000) 213-266
    doi:10.1090/S0002-9947-02-03035-0
  52. Giuseppe Savaré
    Regularity Results for Elliptic Equations in Lipschitz Domains.
    Journal of Functional Analysis 152 (1998) 176-201
    doi:10.1006/jfan.1997.3158
  53. Ricardo H.Nochetto, Giuseppe Savaré, Claudio Verdi
    Error Control of Nonlinear evolution Equations.
    C.R.Acad.Sci.Paris 326, Série I (1998) 1437-1442
    doi:10.1016/S0764-4442(98)80407-2
  54. Giuseppe Savaré, Franco Tomarelli
    Superposition and chain rule for Bounded Hessian functions.
    Advances in Mathematics 140 (1998) 237-281
    doi:10.1006/aima.1998.1770
  55. Giuseppe Savaré
    Parabolic problems with mixed variable lateral conditions: an abstract approach.
    J.Math.Pures Appl. 76 (1997) 321-351
    doi:10.1016/S0021-7824(97)89955-2
  56. Giuseppe Savaré, Augusto Visintin
    Variational convergence of nonlinear diffusion equations: applications to concentrated capacity problems with change of phase.
    Rend.Mat.Acc.Lincei s.9, v.8 (1997) 49-89
  57. Giuseppe Savaré
    Regularity and perturbation results for mixed second order elliptic problems.
    Communications in P.D.E. 22 (1997) 869-899
    doi:10.1080/03605309708821287
  58. Pierluigi Colli, Giuseppe Savaré
    Time discretization of Stefan problems with singular heat flux.
    Quaderni del Dip. di Mat. dell'Università di Torino 1 (1996) 1-12
  59. Ugo Gianazza, Giuseppe Savaré
    Abstract evolution equations on variable domains: an approach by Minimizing Movements.
    Annali della Scuola Normale Superiore di Pisa XXIII (1996) 149-178
  60. Pierluigi Colli, Giuseppe Savaré
    Time discretization of Stefan problems with singular heat flux.
    363 (1996) 16-28
  61. Giuseppe Savaré
    Weak solutions and maximal regularity for abstract evolution inequalities.
    Advances in Mathematical Sciences and Applications 6 (1996) 377-418
  62. Giuseppe Savaré
    On the regularity of the positive part of functions.
    Nonlinear Analysis, T.M.A. 27 (1996) 1055-1074
    doi:10.1016/0362-546X(95)00104-4
  63. Pierluigi Colli, Giuseppe Savaré
    On a class of implicit evolution variational inequalities.
    Differential Integral Equations 8 (1995) 2097-2124
  64. Ugo Gianazza, Giuseppe Savaré
    Some results on Minimizing Movements.
    Rend.Acc.Naz.Sc.dei XL, Mem.Mat 112 (1994) 57-80
  65. Claudio Baiocchi, Giuseppe Savaré
    Singular perturbation and interpolation.
    Mathematical Models and Methods in Applied Sciences 4 (1994) 557-570
    doi:10.1142/S0218202594000315
  66. Giuseppe Savaré, Vincenzo Vespri
    The asymptotic profile of solutions of a class of doubly nonlinear equations.
    Nonlinear Analysis, T.M.A. 22 (1994) 1553-1565
    doi:10.1016/0362-546X(94)90188-0
  67. Giuseppe Savaré
    Some Remarks on Cauchy Problem for Parabolic equations with Dirichlet boundary condition.
    Rend.Ist.Lombardo, Sc.A 128 (1994) 71-91
  68. Ugo Gianazza, Massimo Gobbino, Giuseppe Savaré
    Evolution problems and Minimizing Movements.
    Rend.Mat.Acc.Lincei IX 5 (1994) 289-296
  69. Giuseppe Savaré
    Approximation and regularity of evolution variational inequalities.
    Rend.Acc.Naz.Sc.dei XL, Mem.Mat. 111 (1993) 83-111
  70. Giuseppe Savaré
    A(\Theta)-stable approximations of abstract Cauchy problems.
    Numer. Math. 65 (1993) 319-335
    doi:10.1007/BF01385755
    http://rdcu.be/mE9x (View-only version)
  71. Giuseppe Savaré
    Discretizzazioni A(\Theta)-stabili di equazioni differenziali astratte.
    Calcolo 28 (1991) 205-248

Books

  1. Ambrosio Luigi, Gigli Nicola, Savaré Giuseppe
    Gradient flows in metric spaces and in the space of probability measures
    Lectures in Mathematics ETH Zürich, Birkhäuser Verlag, Basel (2008) x+334
    ../research/optimal_transportation/index.html

Contributions to volumes or proceedings

  1. Daneri Sara, Savaré Giuseppe
    Lecture notes on gradient flows and optimal transport
    in Optimal transportation, Y. Ollivier, H. Pajot, C. Villani (ed.)
    Vol. 413, "London Math. Soc. Lecture Note Ser.", Cambridge Univ. Press, Cambridge (2014) 100--144
    arxiv:1009.3737v1
  2. Luigi Ambrosio, Nicola Gigli, Giuseppe Savaré
    Heat flow and calculus on metric measure spaces with Ricci curvature bounded below - the compact case
    in Analysis and Numerics of Partial Differential Equations, Brezzi F., Colli Franzone P., Gianazza U.P., Gilardi G. (ed.)
    Vol. 4, "INDAM", Springer (2013) 63-116
  3. Luigi Ambrosio, Giuseppe Savaré
    Gradient Flows of Probability Measures
    in Handbook of Evolution Equations, Dafermos C., Feireisl E. (ed.)
    Vol. 3, Elsevier (2006) 1-136
  4. Piero Colli Franzone, Luca F. Pavarino, Giuseppe Savaré
    Computational Electrocardiology: mathematical and numerical modeling.
    in Complex Systems in Biomedicine, A. Quarteroni et al. (ed.)
    Springer-Verlag (2006) 187--241
    doi:10.1007/88-470-0396-2_6
    http://www.springer.com/life+sci/bioinformatics/book/978-88-470-0394-1
  5. Giuseppe Savaré
    Error Estimates for Dissipative Evolution Problems
    in Free Bounday Problems, P.~Colli C.~Verdi A.~Visintin (ed.);
    Vol. 147, "International Series of Numerical Mathematics", Birkhäuser (2003) 281-291

Edited books

  1. Bianchini Stefano, Carlen Eric A., Mielke Alexander, Villani Cédric
    Nonlinear PDE's and applications
    Notes of the C.I.M.E. Summer School held in Cetraro, June 23--28, 2008; Luigi Ambrosio, Giuseppe Savaré (ed.)
    Lecture Notes in Mathematics, Centro Internazionale Matematico Estivo (C.I.M.E.) Summer Schools, Springer, Heidelberg (2011) xiv+224
    doi:10.1007/978-3-642-21861-3