Optimal transport, Cheeger energies and contractivity of dynamic transport distances in extended spaces
From MaRDI portal
Publication:272698
DOI10.1016/j.na.2015.12.006zbMath1337.49075arXiv1506.05932OpenAlexW2963704276MaRDI QIDQ272698
Giuseppe Savaré, Matthias Erbar, Luigi Ambrosio
Publication date: 20 April 2016
Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1506.05932
heat flowoptimal transportCheeger energiesdynamic transport distancesevolution variational inequality
Variational inequalities (49J40) Variational problems in a geometric measure-theoretic setting (49Q20)
Related Items
Tamed spaces -- Dirichlet spaces with distribution-valued Ricci bounds ⋮ A dual formula for the noncommutative transport distance ⋮ Diffusion, optimal transport and Ricci curvature ⋮ Gamma-convergence of Cheeger energies with respect to increasing distances ⋮ Duality properties of metric Sobolev spaces and capacity ⋮ Embedding of \(\mathrm{RCD}^\ast (K,N)\) spaces in \(L^2\) via eigenfunctions ⋮ Sobolev Spaces in Extended Metric-Measure Spaces ⋮ Besov class via heat semigroup on Dirichlet spaces. II: BV functions and Gaussian heat kernel estimates ⋮ The general class of Wasserstein Sobolev spaces: density of cylinder functions, reflexivity, uniform convexity and Clarkson's inequalities ⋮ The intrinsic Hopf-Lax semigroup vs. the intrinsic slope ⋮ Mini-workshop: Variable curvature bounds, analysis and topology on Dirichlet spaces. Abstracts from the mini-workshop held December 5--11, 2021 (hybrid meeting) ⋮ Optimal entropy-transport problems and a new Hellinger-Kantorovich distance between positive measures ⋮ Bakry-Émery conditions on almost smooth metric measure spaces ⋮ Dual graphs and modified Barlow-Bass resistance estimates for repeated barycentric subdivisions ⋮ Rademacher-type theorems and Sobolev-to-Lipschitz properties for strongly local Dirichlet spaces ⋮ Contraction and regularizing properties of heat flows in metric measure spaces ⋮ Gradient flows and evolution variational inequalities in metric spaces. I: structural properties
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Geometry and analysis of Dirichlet forms. II
- Well-posedness of Lagrangian flows and continuity equations in metric measure spaces
- Bakry-Émery curvature-dimension condition and Riemannian Ricci curvature bounds
- Dirichlet forms and symmetric Markov processes.
- Geometry and analysis of Dirichlet forms
- Duality on gradient estimates and Wasserstein controls
- Dirichlet forms and analysis on Wiener space
- Analysis and geometry on configuration spaces
- Differentiability of Lipschitz functions on metric measure spaces
- Small-time Gaussian behavior of symmetric diffusion semigroups
- Generalization of an inequality by Talagrand and links with the logarithmic Sobolev inequality
- A Saint-Venant type principle for Dirichlet forms on discontinuous media
- Is a diffusion process determined by its intrinsic metric?
- Rademacher's theorem on configuration spaces and applications
- Non-contraction of heat flow on Minkowski spaces
- The continuity equation on metric measure spaces
- Rademacher's theorem for Wiener functionals
- 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
- Sobolev spaces in metric measure spaces: reflexivity and lower semicontinuity of slope
- Duality theorems for marginal problems
- Convergence of pointed non-compact metric measure spaces and stability of Ricci curvature bounds and heat flows
- Lecture Notes on Gradient Flows and Optimal Transport
- A dual characterization of length spaces with application to Dirichlet metric spaces
- Eulerian Calculus for the Displacement Convexity in the Wasserstein Distance
- Analysis and Geometry of Markov Diffusion Operators
- A von Neumann Algebra Approach to Quantum Metrics/Quantum Relations
- Optimal Transport
- On the heat flow on metric measure spaces: existence, uniqueness and stability