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2008, 2nd ed., Lectures in mathematics ETH Zürich, ISBN 3764387211, vii, 334
This book is devoted to a theory of gradient flows in spaces which are not necessarily endowed with a natural linear or differentiable structure. It consists... 
Measure theory | Metric spaces | Monotone operators | Differential equations, Partial | Evolution equations, Nonlinear | Mathematics | Differential equations, Parabolic | Probability Theory and Stochastic Processes | Differential Geometry | Measure and Integration
Book
Inventiones mathematicae, ISSN 0020-9910, 2/2014, Volume 195, Issue 2, pp. 289 - 391
This paper is devoted to a deeper understanding of the heat flow and to the refinement of calculus tools on metric measure spaces $(X,\mathsf {d},\mathfrak... 
52C23 | 49J52 | 35K90 | Mathematics, general | Mathematics | 58J35 | 49Q20 | 31C25 | EXISTENCE | MATHEMATICS | EQUATIONS | CURVATURE CONDITIONS | GEOMETRY | Mathematical analysis | Dirichlet problem | Calculus | Heat transmission | Entropy | Density | Curvature | Heat transfer
Journal Article
The Annals of Probability, ISSN 0091-1798, 1/2015, Volume 43, Issue 1, pp. 339 - 404
Journal Article
Inventiones mathematicae, ISSN 0020-9910, 3/2018, Volume 211, Issue 3, pp. 969 - 1117
We develop a full theory for the new class of Optimal Entropy-Transport problems between nonnegative and finite Radon measures in general topological spaces.... 
Mathematics, general | Mathematics | METRIC-MEASURE-SPACES | MATHEMATICS | INEQUALITY | EQUATIONS | CURVATURE-DIMENSION CONDITION | RICCI CURVATURE | GEOMETRY | Entropy | Functionals | Transport | Radon | Mathematics - Optimization and Control
Journal Article
Discrete and Continuous Dynamical Systems- Series A, ISSN 1078-0947, 04/2014, Volume 34, Issue 4, pp. 1641 - 1661
We prove that the linear "heat" flow in a RCD(K, infinity) metric measure space (X, d, m) satisfies a contraction property with respect to every... 
Γ-calculus | Dirichlet forms | Ricci curvature | Metric-measure spaces | Optimal transport | EXISTENCE | MATHEMATICS, APPLIED | STABILITY | INEQUALITY | optimal transport | FOKKER-PLANCK EQUATIONS | MATHEMATICS | metric-measure spaces | MANIFOLDS | Gamma-calculus | GEOMETRY
Journal Article
2005, Lectures in mathematics ETH Zürich, ISBN 9783764324285, vii, 333
This book is devoted to a theory of gradient flows in spaces which are not necessarily endowed with a natural linear or differentiable structure. It consists... 
Measure theory | Differential equations, Parabolic | Metric spaces | Monotone operators | Evolution equations, Nonlinear | Mathematics | Probability Theory and Stochastic Processes | Differential Geometry | Measure and Integration
Book
Journal of Functional Analysis, ISSN 0022-1236, 03/2020, Volume 278, Issue 4, p. 108347
This is the first of a series of papers devoted to a thorough analysis of the class of gradient flows in a metric space that can be characterized by Evolution... 
Evolution variational inequalities | Gradient flows | Metric spaces | Minimizing movements
Journal Article
Duke Mathematical Journal, ISSN 0012-7094, 2014, Volume 163, Issue 7, pp. 1405 - 1490
In this paper, we introduce a synthetic notion of Riemannian Ricci bounds from below for metric measure spaces (X, d, m) which is stable under measured... 
MATHEMATICS | SOBOLEV SPACES | TRANSPORT | INEQUALITIES | STABILITY | COMPACT ALEXANDROV SPACES | FINSLER MANIFOLDS | WASSERSTEIN SPACES | HEAT-FLOW | GRADIENT FLOWS | GEOMETRY | 60J65 | 35K05
Journal Article
Journal of the European Mathematical Society, ISSN 1435-9855, 2016, Volume 18, Issue 9, pp. 2107 - 2165
J. Europ. Math. Soc. 18 (2016) 2107-2165 Balanced Viscosity solutions to rate-independent systems arise as limits of regularized rate-independent flows by... 
Energetic solutions | Existence results | Time discretization | Rate-independent systems | BV solutions | Vanishing viscosity | Mathematics - Analysis of PDEs
Journal Article
Proceedings of the London Mathematical Society, ISSN 0024-6115, 11/2015, Volume 111, Issue 5, pp. 1071 - 1129
The aim of this paper is to discuss convergence of pointed metric measure spaces in the absence of any compactness condition. We propose various definitions,... 
EXISTENCE | MATHEMATICS | TANGENT-CONES | RIEMANNIAN-MANIFOLDS | UNIQUENESS | GEOMETRY | Equivalence | Mathematical analysis | Heat transmission | Spectra | Formulas (mathematics) | Curvature | Heat transfer | Convergence
Journal Article
IEEE Transactions on Information Theory, ISSN 0018-9448, 05/2014, Volume 60, Issue 5, pp. 2687 - 2693
Journal Article
Nonlinear Analysis, ISSN 0362-546X, 05/2016, Volume 137, pp. 77 - 134
We introduce the setting of as a general “Wiener like” framework for optimal transport problems and nonsmooth metric analysis in infinite dimension. After a... 
Evolution variational inequality | Heat flow | Optimal transport | MATHEMATICS | CONFIGURATION-SPACES | MATHEMATICS, APPLIED | METRIC MEASURE-SPACES | DIRICHLET FORMS | FLOWS | RADEMACHERS THEOREM | GEOMETRY | Radon | Dynamics | Mathematical analysis | Dirichlet problem | Links | Nonlinearity | Transport | Optimization
Journal Article
SIAM Journal on Mathematical Analysis, ISSN 0036-1410, 2016, Volume 48, Issue 4, pp. 2869 - 2911
We discuss a new notion of distance on the space of finite and nonnegative measures on Omega subset of R-d, which we call the Hellinger-Kantorovich distance.... 
Dissipation distance | Geodesic curves | Reaction-diffusion equations | Optimal transport | Cone space | Onsager operator | geodesic curves | MATHEMATICS, APPLIED | ENERGY | EULERIAN CALCULUS | LARGE-DEVIATIONS | cone space | optimal transport | dissipation distance | reaction-diffusion equations
Journal Article
Archive for Rational Mechanics and Analysis, ISSN 0003-9527, 1/2018, Volume 227, Issue 1, pp. 423 - 475
We study a model for rate-dependent gradient plasticity at finite strain based on the multiplicative decomposition of the strain tensor, and investigate the... 
Physics, general | Fluid- and Aerodynamics | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | Classical Mechanics | MICROSTRUCTURES | MATHEMATICS, APPLIED | MECHANICS | EVOLUTION | MINIMIZATION | LOWER SEMICONTINUITY | ELASTOPLASTICITY | FORMULATION | MINIMIZERS | Mathematics - Analysis of PDEs
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 09/2019, Volume 277, Issue 6, pp. 1868 - 1957
We investigate a first-order mean field planning problem of the form associated to a convex Hamiltonian with quadratic growth and a monotone interaction term... 
Mean field planning | Kantorovich duality | Superposition principle | Optimal transport | SPACE | MATHEMATICS | GAMES | GEODESICS
Journal Article
Archive for Rational Mechanics and Analysis, ISSN 0003-9527, 2/2018, Volume 227, Issue 2, pp. 477 - 543
We propose the new notion of Visco-Energetic solutions to rate-independent systems $${(X, \mathcal{E},}$$ ( X , E , d) driven by a time dependent energy... 
Physics, general | Fluid- and Aerodynamics | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | Classical Mechanics | EXISTENCE | MATHEMATICS, APPLIED | MECHANICS | QUASI-STATIC EVOLUTION | GROWTH | SYSTEMS | LIMIT | BRITTLE-FRACTURE | MODEL | ELASTOPLASTICITY | FORMULATION | DAMAGE
Journal Article