A new class of transport distances between measures

From MaRDI portal
Publication:1006417

DOI10.1007/s00526-008-0182-5zbMath1157.49042arXiv0803.1235OpenAlexW3101978293MaRDI QIDQ1006417

Giuseppe Savaré, Bruno Nazaret, Jean Dolbeault

Publication date: 24 March 2009

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0803.1235




Related Items (87)

A new perspective on Wasserstein distances for kinetic problemsExistence of solutions for a class of fourth order cross-diffusion systems of gradient flow typeA new transportation distance with bulk/interface interactions and flux penalizationApplications of optimal transportation in the natural sciences. Abstracts from the workshop held February 21--27, 2021 (online meeting)Well-Posedness of an Integro-Differential Model for Active Brownian ParticlesA potential approach for planning mean-field games in one dimensionA Framework for Wasserstein-1-Type MetricsOn gradient flow and entropy solutions for nonlocal transport equations with nonlinear mobilityNonlinear mobility continuity equations and generalized displacement convexityOptimal functional inequalities for fractional operators on the sphere and applicationsGeneral transport problems with branched minimizers as functionals of 1-currents with prescribed boundaryComputational mean-field information dynamics associated with reaction-diffusion equationsOne-dimensional Gagliardo-Nirenberg-Sobolev inequalities: remarks on duality and flowsExistence of weak solutions to a class of fourth order partial differential equations with Wasserstein gradient structureOptimal synchronization problem for a multi-agent systemIncompressible immiscible multiphase flows in porous media: a variational approachGeodesics for a class of distances in the space of probability measuresConvergence of a One-Dimensional Cahn--Hilliard Equation with Degenerate MobilityGeneralized control systems in the space of probability measuresControlling conservation laws. II: Compressible Navier-Stokes equationsEvolution models for mass transportation problemsHomogenisation of dynamical optimal transport on periodic graphsA two-phase two-fluxes degenerate Cahn-Hilliard model as constrained Wasserstein gradient flowGradient flows of modified Wasserstein distances and porous medium equations with nonlocal pressureGeneralized displacement convexity for nonlinear mobility continuity equation and entropy power concavity on Wasserstein space over Riemannian manifoldsNonlocal Wasserstein distance: metric and asymptotic propertiesNonlocal Cross-Interaction Systems on Graphs: Nonquadratic Finslerian Structure and Nonlinear MobilitiesMayer control problem with probabilistic uncertainty on initial positionsGradient flows of the entropy for jump processesThe planning problem in mean field games as regularized mass transportInterpolation between modified logarithmic Sobolev and Poincaré inequalities for quantum Markovian dynamicsNonlocal cross-interaction systems on graphs: energy landscape and dynamicsCosh gradient systems and tiltingThe dynamical Schrödinger problem in abstract metric spacesNumerical analysis of a robust free energy diminishing finite volume scheme for parabolic equations with gradient structureAlgebraic contraction rate for distance between entropy solutions of scalar conservation lawsFractional higher order thin film equation with linear mobility: gradient flow approachStructure Preserving Primal Dual Methods for Gradient Flows with Nonlinear Mobility Transport DistancesNumerical study of Bose-Einstein condensation in the Kaniadakis-Quarati model for bosonsHamilton-Jacobi equations for controlled gradient flows: the comparison principleControlling conservation laws. I: entropy-entropy fluxA fast regularisation of a Newtonian vortex equationOptimal entropy-transport problems and a new Hellinger-Kantorovich distance between positive measuresCahn-Hilliard and thin film equations with nonlinear mobility as gradient flows in weighted-Wasserstein metricsAn interpolating distance between optimal transport and Fisher-Rao metricsUnbalanced optimal transport: dynamic and Kantorovich formulationsCross-diffusion systems with non-zero flux and moving boundary conditionsPoincaré and logarithmic Sobolev inequalities by decomposition of the energy landscapeφ-Entropies: convexity, coercivity and hypocoercivity for Fokker–Planck and kinetic Fokker–Planck equationsInstability, rupture and fluctuations in thin liquid films: theory and computationsVariational methods for evolution. Abstracts from the workshop held November 12--18, 2017Attainability property for a probabilistic target in Wasserstein spacesTime-Optimal Control Problem in the Space of Probability MeasuresOn a fractional thin film equationWhat is a stochastic Hamiltonian process on finite graph? An optimal transport answerStability of Gibbs Posteriors from the Wasserstein Loss for Bayesian Full Waveform InversionFirst-order, stationary mean-field games with congestionThe gradient flow of a generalized Fisher information functional with respect to modified Wasserstein distancesRegularity results for a time-optimal control problem in the space of probability measuresRicci curvature of finite Markov chains via convexity of the entropyA survey on dynamical transport distancesMinimizing movement for a fractional porous medium equation in a periodic settingNonlocal-interaction equation on graphs: gradient flow structure and continuum limitA new transportation distance between non-negative measures, with applications to gradients flows with Dirichlet boundary conditionsGradient flows of the entropy for finite Markov chainsA logarithmic Hardy inequalityOn a class of modified Wasserstein distances induced by concave mobility functions defined on bounded intervalsGradient flow structure for McKean-Vlasov equations on discrete spacesTransport distances and geodesic convexity for systems of degenerate diffusion equationsThe gradient flow structure for incompressible immiscible two-phase flows in porous mediaNonlinear Diffusion Equations and Curvature Conditions in Metric Measure SpacesNon-commutative calculus, optimal transport and functional inequalities in dissipative quantum systemsEntropic and gradient flow formulations for nonlinear diffusionJump processes as generalized gradient flowsA Benamou-Brenier formulation of martingale optimal transportSimulation of multiphase porous media flows with minimising movement and finite volume schemesGeneralized dynamic programming principle and sparse mean-field control problemsDisplacement convexity for first-order mean-field gamesWell-posedness of evolution equations with time-dependent nonlinear mobility: a modified minimizing movement schemeExponential decay of Rényi divergence under Fokker-Planck equationsThe Thin Film Equation with Non-Zero Contact Angle: A Singular Perturbation ApproachHessian transport gradient flowsData-driven gradient flowsDimensional contraction in Wasserstein distance for diffusion semigroups on a Riemannian manifoldThe Linearized Hellinger--Kantorovich DistanceDimensional contraction via Markov transportation distanceVortex formation for a non-local interaction model with Newtonian repulsion and superlinear mobility



Cites Work


This page was built for publication: A new class of transport distances between measures