.png){kind=icon}
.png){kind=icon}
Return
A self-dual polar factorization for vector fields
.png){kind=icon}
OA
AI
DOI：10.1002/cpa.21430.png)
.png){kind=icon}
.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
En 中文
We show that any nondegenerate vector field u in L-infinity (Omega, R-N), where Omega is a bounded domain in R-N, can be written as u(x) = del 1 Pi(S(x), x) for a.e. x is an element of Omega, where S is a measure-preserving point transformation on Omega such that S-2 = I a.e. (an involution), and H : R-N X R-N -> R is a globally Lipschitz antisymmetric convex-concave Hamiltonian. Moreover, u is a monotone map if and only if S can be taken to be the identity, which suggests that our result is a self-dual version of Brenier's polar decomposition for the vector field as u(x) = del(phi) (S(x)), where phi is convex and S is a measure-preserving transformation. We also describe how our polar decomposition can be reformulated as a (self-dual) mass transport problem. (C) 2012 Wiley Periodicals, Inc.
Keywords:
VARIATIONAL RESOLUTIONS
VALUED FUNCTIONS
MONOTONE
EVOLUTIONS
AI Summary
Key information extracted from the uploaded paper, including a brief overview, abstract, background, key highlights, visual analysis, and future outlook.
Journal
IF:
2.7
Papers:
1.5K
Citations:
1.1W