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 …

Recent developments in numerical methods for fully nonlinear second order partial differential equations

X Feng, R Glowinski, M Neilan - siam REVIEW, 2013 - SIAM
This article surveys the recent developments in computational methods for second order
fully nonlinear partial differential equations (PDEs), a relatively new subarea within …

[BOOK][B] The Monge-Ampere equation

CE Gutiérrez, H Brezis - 2001 - Springer
Cristian E. Gutiérrez Second Edition Page 1 Progress in Nonlinear Differential Equations and
Their Applications 89 Cristian E. Gutiérrez The MongeAmpère Equation Second Edition Page …

Chord measures in integral geometry and their Minkowski problems

E Lutwak, D **, D Yang, G Zhang - Communications on Pure …, 2024 - Wiley Online Library
To the families of geometric measures of convex bodies (the area measures of Aleksandrov‐
Fenchel‐Jessen, the curvature measures of Federer, and the recently discovered dual …

Geometric measures in the dual Brunn–Minkowski theory and their associated Minkowski problems

Y Huang, E Lutwak, D Yang, G Zhang - 2016 - projecteuclid.org
A longstanding question in the dual Brunn–Minkowski theory is “What are the dual
analogues of Federer's curvature measures for convex bodies?” The answer to this is …

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 …

The -Aleksandrov problem for -integral curvature

Y Huang, E Lutwak, D Yang… - Journal of Differential …, 2018 - projecteuclid.org
It is shown that within the $ L_p $-Brunn–Minkowski theory that Aleksandrov's integral
curvature has a natural $ L_p $ extension, for all real $ p $. This raises the question of …

On the Lp Gaussian Minkowski problem

Y Feng, S Hu, L Xu - Journal of Differential Equations, 2023 - Elsevier
We will be concerned with the L p Gaussian Minkowski problem in Gaussian probability
space, which amounts to solving a class of Monge-Ampère type equations on the sphere. In …

A necessary and sufficient condition for the existence of entire large solutions to a k-Hessian system

X Zhang, P Chen, Y Wu… - Applied Mathematics …, 2023 - Elsevier
In this paper, we consider the existence of entire large solutions for a k-Hessian system. By
using an iterative technique and some priori estimates, a necessary and sufficient condition …

[HTML][HTML] The Lp dual Minkowski problem for p> 1 and q> 0

KJ Böröczky, F Fodor - Journal of Differential Equations, 2019 - Elsevier
General L p dual curvature measures have recently been introduced by Lutwak, Yang and
Zhang [24]. These new measures unify several other geometric measures of the Brunn …