Exponential convergence for a convexifying equation

Guillaume Carlier; Alfred Galichon

doi:10.1051/cocv/2011163

Exponential convergence for a convexifying equation

Guillaume Carlier, Alfred Galichon

Research output: Contribution to journal › Article › peer-review

Abstract

We consider an evolution equation similar to that introduced by Vese in [Comm. Partial Diff. Eq. 24 (1999) 1573-1591] and whose solution converges in large time to the convex envelope of the initial datum. We give a stochastic control representation for the solution from which we deduce, under quite general assumptions that the convergence in the Lipschitz norm is in fact exponential in time.

Original language	English (US)
Pages (from-to)	611-620
Number of pages	10
Journal	ESAIM - Control, Optimisation and Calculus of Variations
Volume	18
Issue number	3
DOIs	https://doi.org/10.1051/cocv/2011163
State	Published - Jul 1 2012

Keywords

Convex envelope
Nonautonomous gradient flows
Stochastic control representation
Viscosity solutions

ASJC Scopus subject areas

Control and Systems Engineering
Control and Optimization
Computational Mathematics

Access to Document

10.1051/cocv/2011163

Cite this

@article{c213d6cb2fd2485281d34d51047214d5,

title = "Exponential convergence for a convexifying equation",

abstract = "We consider an evolution equation similar to that introduced by Vese in [Comm. Partial Diff. Eq. 24 (1999) 1573-1591] and whose solution converges in large time to the convex envelope of the initial datum. We give a stochastic control representation for the solution from which we deduce, under quite general assumptions that the convergence in the Lipschitz norm is in fact exponential in time.",

keywords = "Convex envelope, Nonautonomous gradient flows, Stochastic control representation, Viscosity solutions",

author = "Guillaume Carlier and Alfred Galichon",

year = "2012",

month = jul,

day = "1",

doi = "10.1051/cocv/2011163",

language = "English (US)",

volume = "18",

pages = "611--620",

journal = "ESAIM - Control, Optimisation and Calculus of Variations",

issn = "1292-8119",

publisher = "EDP Sciences",

number = "3",

}

TY - JOUR

T1 - Exponential convergence for a convexifying equation

AU - Carlier, Guillaume

AU - Galichon, Alfred

PY - 2012/7/1

Y1 - 2012/7/1

N2 - We consider an evolution equation similar to that introduced by Vese in [Comm. Partial Diff. Eq. 24 (1999) 1573-1591] and whose solution converges in large time to the convex envelope of the initial datum. We give a stochastic control representation for the solution from which we deduce, under quite general assumptions that the convergence in the Lipschitz norm is in fact exponential in time.

AB - We consider an evolution equation similar to that introduced by Vese in [Comm. Partial Diff. Eq. 24 (1999) 1573-1591] and whose solution converges in large time to the convex envelope of the initial datum. We give a stochastic control representation for the solution from which we deduce, under quite general assumptions that the convergence in the Lipschitz norm is in fact exponential in time.

KW - Convex envelope

KW - Nonautonomous gradient flows

KW - Stochastic control representation

KW - Viscosity solutions

UR - http://www.scopus.com/inward/record.url?scp=84871489416&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84871489416&partnerID=8YFLogxK

U2 - 10.1051/cocv/2011163

DO - 10.1051/cocv/2011163

M3 - Article

AN - SCOPUS:84871489416

SN - 1292-8119

VL - 18

SP - 611

EP - 620

JO - ESAIM - Control, Optimisation and Calculus of Variations

JF - ESAIM - Control, Optimisation and Calculus of Variations

IS - 3

ER -

Exponential convergence for a convexifying equation

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this