Giuseppe Savaré

Short CV

After graduating in Mathematics in 1988, Giuseppe Savaré obtained a research position at the CNR Institute for Applied Mathematics and Information Technologies ``Enrico Magenes’’ in 1990. Since 2000 he is full professor of Mathematical Analysis at the Department of Mathematics of the University of Pavia. He is also fellow of the Istituto Lombardo – Accademia di Scienze e Lettere and director of the PhD Higher Education School of the University of Pavia. His research activity concerns variational methods for evolution problems, in particular gradient flows and rate-independent models, and their interplay with optimal transport, measure theoretic tools and analysis in metric spaces.

Selected Awards

  • 2016, Invited Speaker at the 7th European Congress of Mathematics (7ECM), Berlin: section “Analysis and PDEs”.
  • 2011, Ennio De Giorgi Prize, first edition; awarded by the Italian Mathematical Union to a mathematician under 45 years of age.
  • 1994, Gioachino Japichino Prize, awarded by the Accademia Nazionale dei Lincei to a mathematician (under 30 years of age) for a relevant publication in Analysis.

Research Interests

Gradient flows, rate independent evolutions, nonlinear diffusion PDE’s, Optimal transport and entropy-transport problems, analysis in metric spaces, metric-measure spaces with lower Ricci curvature bounds.

Selected Publications

  1. Gradient flows in metric spaces and in the space of probability measures (with L. Ambrosio, N. Gigli) Lectures in Mathematics ETH Zürich. Birkhäuser Verlag, Basel, 2005 (second edition 2008).
  2. Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below (with L. Ambrosio, N. Gigli). Invent. Math. 195 (2014), 289–391.
  3. Metric measure spaces with Riemannian Ricci curvature bounded from below (with L. Ambrosio, N. Gigli). Duke Math. J., 163 (2014):1405–1490.
  4. Optimal entropy-transport problems and a new Hellinger-Kantorovich distance between positive measures (with M. Liero, A. Mielke). Invent. Math. 211 (2018), no. 3, 969–1117.
  5. Bakry-Émery curvature-dimension condition and Riemannian Ricci curvature bounds (with L. Ambrosio, N. Gigli). Annals of Probability, 43, (2015): 339–404.
  6. Balanced viscosity (BV) solutions to infinite-dimensional rate-independent systems (with A. Mielke, R. Rossi). JEMS, 18 (2016) 2107–2165.
  7. On the duality between p-Modulus and probability measures (with L. Ambrosio, S. Di Marino). JEMS, 17 (2015) 1817–1853.
  8. The Wasserstein gradient flow of the Fisher information and the quantum drift-diffusion equation (with U. Gianazza, G. Toscani). Arch. Ration. Mech. Anal., 194 (2009):133–220.
  9. A posteriori error estimates for variable time-step discretizations of nonlinear evolution equations (with R.H. Nochetto, C. Verdi). Comm. Pure Appl. Math., 53 (2000):525–589.
  10. Regularity results for elliptic equations in Lipschitz domains J. Funct. Anal., 152 (1998):176–201.

Publications as TUM-IAS Fellow


  • Ambrosio, Luigi; ; Savaré, Giuseppe; ; ; ; ;: Duality properties of metric Sobolev spaces and capacity. Mathematics in Engineering 3 (1), 2021, 1-31 mehr…
  • Ambrosio, Luigi; Fornasier, Massimo; Morandotti, Marco; Savaré, Giuseppe: Spatially Inhomogeneous Evolutionary Games. Communications on Pure and Applied Mathematics 74 (7), 2021, 1353-1402 mehr…
  • Naldi, Emanuele; Savaré, Giuseppe: Weak topology and Opial property in Wasserstein spaces, with applications to Gradient Flows and Proximal Point Algorithms of geodesically convex functionals. 2021 mehr…


  • Cavagnari, Giulia; Lisini, Stefano; Orrieri, Carlo; Savaré, Giuseppe: Lagrangian, Eulerian and Kantorovich formulations of multi-agent optimal control problems: Equivalence and Gamma-convergence. 2020 mehr…


  • Savaré, Giuseppe: Sobolev spaces in extended metric-measure spaces. 2019 mehr…


  • Fornasier, Massimo; Lisini, Stefano; Orrieri, Carlo; Savaré, Giuseppe: Mean-field optimal control as Gamma-limit of finite agent controls. arXiv, 2018 mehr…