Dealing with moment measures via entropy and optimal transport

DOI10.1016/j.jfa.2016.04.009zbMath1343.49075arXiv1507.04187OpenAlexW2963641422MaRDI QIDQ285820

Filippo Santambrogio

Publication date: 19 May 2016

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1507.04187

zbMATH Keywords

entropyoptimal transportmoment measuresdisplacement convexityBrenier maplog-concave measureslower semi-continuity

Mathematics Subject Classification ID

Measure-preserving transformations (28D05) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Variational problems in a geometric measure-theoretic setting (49Q20) Regularity of solutions in optimal control (49N60) Methods involving semicontinuity and convergence; relaxation (49J45)

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Cites Work

• Duality in nonconvex optimization
• A duality principle for non-convex optimisation and the calculus of variations
• A convexity principle for interacting gases
• \(W^{2,1}\) regularity for solutions of the Monge-Ampère equation
• Moment measures
• Optimal transport for applied mathematicians. Calculus of variations, PDEs, and modeling
• Transport and concentration problems with interaction effects
• Optimal Transport and Cournot-Nash Equilibria
• EXISTENCE AND UNIQUENESS OF EQUILIBRIUM FOR A SPATIAL MODEL OF SOCIAL INTERACTIONS*
• The Monge–Ampère equation and its link to optimal transportation
• A Mass Transportation Model for the Optimal Planning of an Urban Region
• New lower semicontinuity results for nonconvex functionals defined on measures
• Optimal Transport
• Monotonicity properties of optimal transportation and the FKG and related inequalities
• \(BV\) estimates in optimal transportation and applications
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