Second order derivative of a functional associated to an optimal transport map

DOI10.1007/s00605-023-01856-9zbMath1526.46049OpenAlexW4362554148MaRDI QIDQ6097056

Unnamed Author, Joaquín Delgado

Publication date: 9 June 2023

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00605-023-01856-9

zbMATH Keywords

optimal transport mapconvex conjugateMonge's potentialsecond order Gâteaux differentiability

Mathematics Subject Classification ID

Fréchet and Gateaux differentiability in optimization (49J50) Applications of functional analysis in optimization, convex analysis, mathematical programming, economics (46N10) Derivatives of functions in infinite-dimensional spaces (46G05)

Cites Work

• Second derivatives of convex functions in the sense of A.\ D.\ Aleksandrov on infinite-dimensional spaces with measure
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• The Regularity of Mappings with a Convex Potential
• Second order differentiability of integral functionals on Sobolev spaces and L2-spaces.
• Second Order Differentiability of Convex Functions in Banach Spaces
• Minimizing Flows for the Monge--Kantorovich Problem
• Second order differentiability and Lipschitz smooth points of convex functionals
• Optimal Transport
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