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
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).
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.
Metric measure spaces with Riemannian Ricci curvature bounded from below (with L. Ambrosio, N. Gigli). Duke Math. J., 163 (2014):1405–1490.
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.
Bakry-Émery curvature-dimension condition and Riemannian Ricci curvature bounds (with L. Ambrosio, N. Gigli). Annals of Probability, 43, (2015): 339–404.
Balanced viscosity (BV) solutions to infinite-dimensional rate-independent systems (with A. Mielke, R. Rossi). JEMS, 18 (2016) 2107–2165.
On the duality between p-Modulus and probability measures (with L. Ambrosio, S. Di Marino). JEMS, 17 (2015) 1817–1853.
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.
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.
Regularity results for elliptic equations in Lipschitz domains J. Funct. Anal., 152 (1998):176–201.
Savaré, Giuseppe; Sodini, Giacomo Enrico: A relaxation viewpoint to Unbalanced Optimal Transport: duality, optimality and Monge formulation. , 2024 mehr…
2023
Cavagnari, Giulia; Savaré, Giuseppe; Sodini, Giacomo Enrico: Extension of monotone operators and Lipschitz maps invariant for a group of isometries. Canadian Journal of Mathematics, 2023, 1-38 mehr…
Cavagnari, Giulia; Savaré, Giuseppe; Sodini, Giacomo Enrico: A Lagrangian approach to totally dissipative evolutions in Wasserstein spaces. , 2023 mehr…
Fornasier, Massimo; Heid, Pascal; Sodini, Giacomo Enrico: Approximation Theory, Computing, and Deep Learning on the Wasserstein Space. , 2023 mehr…
Liero, Matthias; Mielke, Alexander; Savaré, Giuseppe: Fine Properties of Geodesics and Geodesic $$\lambda $$-Convexity for the Hellinger–Kantorovich Distance. Archive for Rational Mechanics and Analysis 247 (6), 2023 mehr…
Matthes, Daniel; Rott, Eva-Maria; Savaré, Giuseppe; Schlichting, André: A structure preserving discretization for the Derrida-Lebowitz-Speer-Spohn equation based on diffusive transport. , 2023 mehr…
Mazzoleni, Dario; ; Savaré, Giuseppe;: $ L^2 $-Gradient flows of spectral functionals. Discrete and Continuous Dynamical Systems 43 (3&4), 2023, 1560-1594 mehr…
2022
Cavagnari, Giulia; Lisini, Stefano; Orrieri, Carlo; Savaré, Giuseppe: Lagrangian, Eulerian and Kantorovich formulations of multi-agent optimal control problems: Equivalence and Gamma-convergence. Journal of Differential Equations 322, 2022, 268-364 mehr…
Cavagnari, Giulia; Savaré, Giuseppe; Sodini, Giacomo Enrico: Dissipative probability vector fields and generation of evolution semigroups in Wasserstein spaces. Probability Theory and Related Fields, 2022 mehr…
Fornasier, Massimo; Savaré, Giuseppe; Sodini, Giacomo: Density of subalgebras of Lipschitz functions in metric Sobolev spaces and applications to Wasserstein Sobolev spaces. , 2022 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. Rendiconti Lincei - Matematica e Applicazioni 32 (4), 2022, 725-750 mehr…
Peletier, Mark A.; Rossi, Riccarda; Savaré, Giuseppe; Tse, Oliver: Jump processes as generalized gradient flows. Calculus of Variations and Partial Differential Equations 61 (1), 2022 mehr…
Sodini, Giacomo Enrico: The general class of Wasserstein Sobolev spaces: density of cylinder functions, reflexivity, uniform convexity and Clarkson's inequalities. , 2022 mehr…
Sodini, Giacomo; Savaré, Giuseppe: A Simple Relaxation Approach to Duality for Optimal Transport Problems in Completely Regular Spaces. Journal of Convex Analysis 29, 2022, 1-12 mehr…
2021
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…
Savaré, Giuseppe: Sobolev Spaces in Extended Metric-Measure Spaces. In: Lecture Notes in Mathematics. Springer International Publishing, 2021 mehr…
2020
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…
2019
Savaré, Giuseppe: Sobolev spaces in extended metric-measure spaces. 2019 mehr…
2018
Fornasier, Massimo; Lisini, Stefano; Orrieri, Carlo; Savaré, Giuseppe: Mean-field optimal control as Gamma-limit of finite agent controls. arXiv, 2018 mehr…
