Sharp PDE estimates for random two-dimensional bipartite matching with power cost function

Dario Trevisan, Federico Vitillaro, Luigi Ambrosio

Publication date: 13 December 2024

Published in: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni (Search for Journal in Brave)

zbMATH Keywords

optimal transport \(q\)-Laplacian Hopf-Lax semigroup

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Existence of optimal solutions to problems involving randomness (49J55)

Cites Work

Density of Lipschitz functions and equivalence of weak gradients in metric measure spaces
On optimal matchings
A PDE approach to a 2-dimensional matching problem
Random assignment problems on \(2d\) manifolds
A simple Fourier analytic proof of the AKT optimal matching theorem
On the quadratic random matching problem in two-dimensional domains
A fluctuation result for the displacement in the optimal matching problem
Finer estimates on the \(2\)-dimensional matching problem
On the optimal map in the 2-dimensional random matching problem
Regularity for quasilinear equations on degenerate singular sets
On the curvature and heat flow on Hamiltonian systems
On the subspaces of \(L^p\) \((p > 2)\) spanned by sequences of independent random variables
Euclidean random matching in 2D for non-constant densities
On the equivalence of viscosity solutions and weak solutions for a quasi-linear equation
A New Proof for the Equivalence of Weak and Viscosity Solutions for thep-Laplace Equation
Quantitative Linearization Results for the <scp>Monge‐Ampère</scp> Equation
User’s guide to viscosity solutions of second order partial differential equations
Lectures on Optimal Transport
Comparison between W₂ distance and Ḣ⁻¹ norm, and Localization of Wasserstein distance
There is no stationary cyclically monotone Poisson matching in 2d
Optimal Matching of Random Samples and Rates of Convergence of Empirical Measures
Geometric linearisation for optimal transport with strongly \(p\)-convex cost
There is no stationary \(p\)-cyclically monotone Poisson matching in 2d
Annealed quantitative estimates for the quadratic 2D-discrete random matching problem

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