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Optimal Entropy-Transport problems and a new Hellinger–Kantorovich distance between positive measures

Inventiones mathematicae, 2018-03, Vol.211 (3), p.969-1117

2018

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Convergence of pointed non‐compact metric measure spaces and stability of Ricci curvature bounds and heat flows

Proceedings of the London Mathematical Society, 2015-11, Vol.111 (5), p.1071-1129

2015

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Jump processes as generalized gradient flows

Calculus of variations and partial differential equations, 2022-02, Vol.61 (1), Article 33

2022

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Density of Lipschitz functions and equivalence of weak gradients in metric measure spaces

Revista matemática iberoamericana, 2013-01, Vol.29 (3), p.969-996

2013

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Nonsmooth analysis of doubly nonlinear evolution equations

Calculus of variations and partial differential equations, 2013-01, Vol.46 (1-2), p.253-310

2013

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A new class of transport distances between measures

Calculus of variations and partial differential equations, 2009-02, Vol.34 (2), p.193-231

2009

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The Wasserstein Gradient Flow of the Fisher Information and the Quantum Drift-diffusion Equation

Archive for rational mechanics and analysis, 2009-10, Vol.194 (1), p.133-220

2009

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A Family of Nonlinear Fourth Order Equations of Gradient Flow Type

Communications in partial differential equations, 2009-11, Vol.34 (11), p.1352-1397

2009

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EULERIAN CALCULUS FOR THE DISPLACEMENT CONVEXITY IN THE WASSERSTEIN DISTANCE

SIAM journal on mathematical analysis, 2008-01, Vol.40 (3), p.1104-1122

2008

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Self-improvement of the Bakry-Émery condition and Wasserstein contraction of the heat flow in $RCD (K, \infty)$ metric measure spaces

Discrete and continuous dynamical systems. Series A, 2014-04, Vol.34 (4), p.1641-1661

Savaré, Giuseppe

2014

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Duality properties of metric Sobolev spaces and capacity

Mathematics in engineering, 2021-01, Vol.3 (1), p.1-31

2021

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Existence and stability for Fokker–Planck equations with log-concave reference measure

Probability theory and related fields, 2009-11, Vol.145 (3-4), p.517-564

2009

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Gradient flows and diffusion semigroups in metric spaces under lower curvature bounds

Comptes rendus. Mathématique, 2007-08, Vol.345 (3), p.151-154

SAVARE, Giuseppe

2007

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Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below

Inventiones mathematicae, 2014-02, Vol.195 (2), p.289-391

2014

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Metric measure spaces with Riemannian Ricci curvature bounded from below

Duke mathematical journal, 2014-05, Vol.163 (7), p.1405-1490

2014

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Nonlinear Diffusion Equations and Curvature Conditions in Metric Measure Spaces

Memoirs of the American Mathematical Society, 2019-11, Vol.262 (1270)

2019

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BAKRY–ÉMERY CURVATURE-DIMENSION CONDITION AND RIEMANNIAN RICCI CURVATURE BOUNDS

The Annals of applied probability, 2015-01, Vol.43 (1), p.339-404

2015

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Lagrangian, Eulerian and Kantorovich formulations of multi-agent optimal control problems: Equivalence and Gamma-convergence

Journal of Differential Equations, 2022-06, Vol.322, p.268-364

2022

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Optimal Transport in Competition with Reaction: The Hellinger--Kantorovich Distance and Geodesic Curves

SIAM journal on mathematical analysis, 2016-01, Vol.48 (4), p.2869-2911

2016

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A variational approach to the mean field planning problem

Journal of functional analysis, 2019-09, Vol.277 (6), p.1868-1957

2019

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A relaxation viewpoint to Unbalanced Optimal Transport: Duality, optimality and Monge formulation

Journal de mathématiques pures et appliquées, 2024-08, Vol.188, p.114-178

2024

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Balanced Viscosity (BV) solutions to infinite-dimensional rate-independent systems

Journal of the European Mathematical Society : JEMS, 2016-01, Vol.18 (9), p.2107-2165

2016

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Density of subalgebras of Lipschitz functions in metric Sobolev spaces and applications to Wasserstein Sobolev spaces

Journal of functional analysis, 2023-12, Vol.285 (11), p.110153, Article 110153

2023

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Fine Properties of Geodesics and Geodesic λ-Convexity for the Hellinger–Kantorovich Distance

Archive for rational mechanics and analysis, 2023-12, Vol.247 (6), p.112-112, Article 112

2023

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L^2 $-Gradient flows of spectral functionals

Discrete and continuous dynamical systems. Series A, 2023, Vol.43 (3&4), p.1560-1594

2023

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Optimal Entropy-Transport problems and a new Hellinger–Kantorovich distance between positive measures

Convergence of pointed non‐compact metric measure spaces and stability of Ricci curvature bounds and heat flows

Jump processes as generalized gradient flows

Density of Lipschitz functions and equivalence of weak gradients in metric measure spaces

Nonsmooth analysis of doubly nonlinear evolution equations

A new class of transport distances between measures

The Wasserstein Gradient Flow of the Fisher Information and the Quantum Drift-diffusion Equation

A Family of Nonlinear Fourth Order Equations of Gradient Flow Type

EULERIAN CALCULUS FOR THE DISPLACEMENT CONVEXITY IN THE WASSERSTEIN DISTANCE

Self-improvement of the Bakry-Émery condition and Wasserstein contraction of the heat flow in $RCD (K, \infty)$ metric measure spaces

Duality properties of metric Sobolev spaces and capacity

Existence and stability for Fokker–Planck equations with log-concave reference measure

Gradient flows and diffusion semigroups in metric spaces under lower curvature bounds

Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below

Metric measure spaces with Riemannian Ricci curvature bounded from below

Nonlinear Diffusion Equations and Curvature Conditions in Metric Measure Spaces

BAKRY–ÉMERY CURVATURE-DIMENSION CONDITION AND RIEMANNIAN RICCI CURVATURE BOUNDS

Lagrangian, Eulerian and Kantorovich formulations of multi-agent optimal control problems: Equivalence and Gamma-convergence

Optimal Transport in Competition with Reaction: The Hellinger--Kantorovich Distance and Geodesic Curves

A variational approach to the mean field planning problem

A relaxation viewpoint to Unbalanced Optimal Transport: Duality, optimality and Monge formulation

Balanced Viscosity (BV) solutions to infinite-dimensional rate-independent systems

Density of subalgebras of Lipschitz functions in metric Sobolev spaces and applications to Wasserstein Sobolev spaces

Fine Properties of Geodesics and Geodesic λ-Convexity for the Hellinger–Kantorovich Distance

L^2 $-Gradient flows of spectral functionals

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