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, viscosity solutions, stochastic control representation, nonautonomous gradient flows
@article{COCV_2012__18_3_611_0,
author = {Carlier, Guillaume and Galichon, Alfred},
title = {Exponential convergence for a convexifying equation},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {611--620},
year = {2012},
publisher = {EDP Sciences},
volume = {18},
number = {3},
doi = {10.1051/cocv/2011163},
mrnumber = {3041657},
zbl = {1255.35041},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2011163/}
}
TY - JOUR AU - Carlier, Guillaume AU - Galichon, Alfred TI - Exponential convergence for a convexifying equation JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2012 SP - 611 EP - 620 VL - 18 IS - 3 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2011163/ DO - 10.1051/cocv/2011163 LA - en ID - COCV_2012__18_3_611_0 ER -
%0 Journal Article %A Carlier, Guillaume %A Galichon, Alfred %T Exponential convergence for a convexifying equation %J ESAIM: Control, Optimisation and Calculus of Variations %D 2012 %P 611-620 %V 18 %N 3 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/cocv/2011163/ %R 10.1051/cocv/2011163 %G en %F COCV_2012__18_3_611_0
Carlier, Guillaume; Galichon, Alfred. Exponential convergence for a convexifying equation. ESAIM: Control, Optimisation and Calculus of Variations, Tome 18 (2012) no. 3, pp. 611-620. doi: 10.1051/cocv/2011163
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