The Monge-Kantorovich problem: achievements, connections, and perspectives

VI Bogachev, AV Kolesnikov - Russian Mathematical Surveys, 2012 - iopscience.iop.org
This article gives a survey of recent research related to the Monge-Kantorovich problem.
Principle results are presented on the existence of solutions and their properties both in the …

[LIBRO][B] Topics in optimal transportation

C Villani - 2021 - books.google.com
This is the first comprehensive introduction to the theory of mass transportation with its many—
and sometimes unexpected—applications. In a novel approach to the subject, the book both …

[LIBRO][B] Optimal transport: old and new

C Villani - 2009 - Springer
At the close of the 1980s, the independent contributions of Yann Brenier, Mike Cullen and
John Mather launched a revolution in the venerable field of optimal transport founded by G …

The Monge–Ampère equation and its link to optimal transportation

G De Philippis, A Figalli - Bulletin of the American Mathematical Society, 2014 - ams.org
AMS :: Bulletin of the American Mathematical Society Skip to Main Content American
Mathematical Society American Mathematical Society MathSciNet Bookstore Publications …

Задача Монжа–Канторовича: достижения, связи и перспективы

ВИ Богачев, АВ Колесников - Успехи математических наук, 2012 - mathnet.ru
В статье дается обзор недавних исследований, связанных с задачей Монжа-
Канторовича. Приведены основные результаты о существовании решений и их …

Five lectures on optimal transportation: geometry, regularity and applications

RJ McCann, N Guillen - Analysis and geometry of metric measure …, 2011 - books.google.com
In this series of lectures we introduce the Monge–Kantorovich problem of optimally
transporting one distribution of mass onto another, where optimality is measured against a …

Hölder continuity and injectivity of optimal maps

A Figalli, YH Kim, RJ McCann - Archive for Rational Mechanics and …, 2013 - Springer
Consider transportation of one distribution of mass onto another, chosen to optimize the total
expected cost, where cost per unit mass transported from x to y is given by a smooth function …

On the existence of radial solutions to a nonlinear k-Hessian system with gradient term

G Wang, Z Zhang, B Ahmad - Nonlinear Analysis: Real World Applications, 2025 - Elsevier
This paper investigates a nonlinear k-Hessian system with gradient term by the monotone
iterative method. We obtain the existence criteria for the entire positive radial solution. The …

Pointwise estimates and regularity in geometric optics and other generated Jacobian equations

N Guillen, J Kitagawa - Communications on Pure and Applied …, 2017 - Wiley Online Library
The study of reflector surfaces in geometric optics necessitates the analysis of certain
nonlinear equations of Monge‐Ampère type known as generated Jacobian equations. This …

On weighted Blaschke--Santalo and strong Brascamp--Lieb inequalities

A Colesanti, A Kolesnikov, G Livshyts… - arxiv preprint arxiv …, 2024 - arxiv.org
arxiv:2409.11503v1 [math.FA] 17 Sep 2024 Page 1 arxiv:2409.11503v1 [math.FA] 17 Sep
2024 On weighted Blaschke–Santaló and strong Brascamp–Lieb inequalities Andrea …