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

From MaRDI portal
Publication:373507

DOI10.4171/RMI/746zbMath1287.46027arXiv1111.3730WikidataQ125941223 ScholiaQ125941223MaRDI QIDQ373507

Nicola Gigli, Giuseppe Savaré, Luigi Ambrosio

Publication date: 17 October 2013

Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1111.3730




Related Items (only showing first 100 items - show all)

On master test plans for the space of BV functionsFirst-order heat content asymptotics on \(\mathsf{RCD} (K, N)\) spacesCalculus and fine properties of functions of bounded variation on RCD spacesExtensions and approximations of Banach-valued Sobolev functionsHeat kernels, stochastic processes and functional inequalities. Abstracts from the workshop held October 30 -- November 5, 2022Non-Hilbertian tangents to Hilbertian spacesStability of Sobolev inequalities on Riemannian manifolds with Ricci curvature lower boundsThe Neumann and Dirichlet problems for the total variation flow in metric measure spacesThe normal contraction property for non-bilinear Dirichlet formsThe Cheeger cut and Cheeger problem in metric measure spacesExtremal of log-Sobolev functionals and Li-Yau estimate on \(\mathrm{RCD}^* (K,N)\) spacesUniversal infinitesimal Hilbertianity of sub-Riemannian manifoldsThe general class of Wasserstein Sobolev spaces: density of cylinder functions, reflexivity, uniform convexity and Clarkson's inequalitiesFailure of curvature-dimension conditions on sub-Riemannian manifolds via tangent isometriesSharp log-Sobolev inequalities in \(\mathsf{CD}(0, N)\) spaces with applicationsCurvewise characterizations of minimal upper gradients and the construction of a Sobolev differentialPlans on measures and \textit{AM}-modulusIndependence on \(p\) of weak upper gradients on \(\mathsf{RCD}\) spacesHeat kernel bounds on metric measure spaces and some applicationsLecture notes on differential calculus on \(\mathsf{RCD}\) spacesIsoperimetric sets in spaces with lower bounds on the Ricci curvatureFunctions of bounded variation and the \(AM\)-modulus in \(\mathbb{R}^n\)Time-smoothing for parabolic variational problems in metric measure spacesOn BV functions and essentially bounded divergence-measure fields in metric spacesA reverse Hölder inequality for first eigenfunctions of the Dirichlet Laplacian on 𝑅𝐶𝐷(𝐾,𝑁) spacesThe $p$-weak gradient depends on $p$\(q\)-heat flow and the gradient flow of the Renyi entropy in the \(p\)-Wasserstein spaceBoundary behavior of harmonic functions on metric measure spaces with non-negative Ricci curvatureInfinitesimal structure of differentiability spaces, and metric differentiationConvergence of pointed non-compact metric measure spaces and stability of Ricci curvature bounds and heat flowsOn the structure of RCD spaces with upper curvature boundsGamma-convergence of Cheeger energies with respect to increasing distancesOn quotients of spaces with Ricci curvature bounded belowTesting the Sobolev property with a single test planRigidity and almost rigidity of Sobolev inequalities on compact spaces with lower Ricci curvature boundsSobolev spaces on warped productsRecognizing the flat torus among \(\mathsf{RCD}^*(0,N)\) spaces via the study of the first cohomology groupOn the \(p\)-Laplacian evolution equation in metric measure spacesNew characterizations of Ricci curvature on RCD metric measure spacesThe Cartan, Choquet and Kellogg properties for the fine topology on metric spacesOptimal transport, gradient estimates, and pathwise Brownian coupling on spaces with variable Ricci boundsDuality properties of metric Sobolev spaces and capacityA first-order condition for the independence on \(p\) of weak gradientsOptimal transport and large number of particlesOn the differential structure of metric measure spaces and applicationsNon-embedding theorems of nilpotent Lie groups and sub-Riemannian manifoldsRadial processes on \(\mathsf{RCD}^\ast(K,N)\) spacesCoarea inequality for monotone functions on metric surfacesSobolev Spaces in Extended Metric-Measure SpacesBrief Survey on Functions of Bounded Variation (BV) in Metric SettingDensity of subalgebras of Lipschitz functions in metric Sobolev spaces and applications to Wasserstein Sobolev spacesSharp \(p\)-Poincaré inequalities under measure contraction propertyLocal vector measuresConstancy of the dimension in codimension one and locality of the unit normal on $\RCD(K,N)$ spacesA short proof of the existence of master test plansDensity of Lipschitz functions in energyHigher dimensional holonomy map for rules submanifolds in graded manifoldsMonotonicity formulas for harmonic functions in \(\mathrm{RCD}(0,N)\) spacesThe rigidity of sharp spectral gap in non-negatively curved spacesHamilton's gradient estimates and a monotonicity formula for heat flows on metric measure spacesA version of Stokes's theorem using test curvesRegularity of Lagrangian flows over \(\operatorname{RCD}^*(K, N)\) spacesCD meets CATSobolev functions on varifoldsCalculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from belowTrace theorems for functions of bounded variation in metric spacesA short proof of the infinitesimal hilbertianity of the weighted Euclidean spaceNew characterizations of Sobolev metric spacesThe Hopf-Lax formula in Carnot groups: a control theoretic approachHamilton Jacobi equations on metric spaces and transport entropy inequalitiesMonotonicity and rigidity of the \(\mathcal{W}\)-entropy on \(\mathsf{RCD} (0, N)\) spacesInscribed radius bounds for lower Ricci bounded metric measure spaces with mean convex boundaryQuasi-continuous vector fields on RCD spacesOn the curvature and heat flow on Hamiltonian systemsAbsolutely continuous curves in extended Wasserstein−Orlicz spacesBakry-Émery curvature-dimension condition and Riemannian Ricci curvature boundsOn the duality between \(p\)-modulus and probability measuresSpace-time Wasserstein controls and Bakry-Ledoux type gradient estimatesMetric viscosity solutions of Hamilton-Jacobi equations depending on local slopesSharp heat kernel bounds and entropy in metric measure spacesLocal Li-Yau's estimates on \(RCD^\ast(K,N)\) metric measure spacesKorevaar-Schoen's energy on strongly rectifiable spacesQuasiopen and \(p\)-path open sets, and characterizations of quasicontinuityNonsmooth differential geometry– An approach tailored for spaces with Ricci curvature bounded from belowSharp Poincaré inequalities under Measure Contraction PropertyOn interpolation and curvature via Wasserstein geodesics\{Euclidean, metric, and Wasserstein\} gradient flows: an overviewAbstract and concrete tangent modules on Lipschitz differentiability spacesEquivalent definitions of \(BV\) space and of total variation on metric measure spacesRegularization of Newtonian functions on metric spaces via weak boundedness of maximal operatorsNotions of Dirichlet problem for functions of least gradient in metric measure spacesOn Cheeger and Sobolev differentials in metric measure spacesLocal gradient estimates for heat equation on 𝑅𝐶𝐷*(𝑘,𝑛) metric measure spacesLocal and semilocal Poincaré inequalities on metric spacesStratified spaces and synthetic Ricci curvature boundsDifferential of metric valued Sobolev mapsThe space of functions of bounded variation on curves in metric measure spacesGlobal Lipschitz extension preserving local constantsStability of metric measure spaces with integral Ricci curvature boundsKorevaar-Schoen's directional energy and Ambrosio's regular Lagrangian flows



Cites Work


This page was built for publication: Density of Lipschitz functions and equivalence of weak gradients in metric measure spaces