Voir la notice de l'article provenant de la source Numdam
We provide a deterministic-control-based interpretation for a broad class of fully nonlinear parabolic and elliptic PDEs with continuous Neumann boundary conditions in a smooth domain. We construct families of two-person games depending on a small parameter ε which extend those proposed by Kohn and Serfaty [21]. These new games treat a Neumann boundary condition by introducing some specific rules near the boundary. We show that the value function converges, in the viscosity sense, to the solution of the PDE as ε tends to zero. Moreover, our construction allows us to treat both the oblique and the mixed type Dirichlet-Neumann boundary conditions.
@article{COCV_2013__19_4_1109_0,
author = {Daniel, Jean-Paul},
title = {A game interpretation of the {Neumann} problem for fully nonlinear parabolic and elliptic equations},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {1109--1165},
publisher = {EDP-Sciences},
volume = {19},
number = {4},
year = {2013},
doi = {10.1051/cocv/2013047},
mrnumber = {3182683},
zbl = {1283.49028},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2013047/}
}
TY - JOUR AU - Daniel, Jean-Paul TI - A game interpretation of the Neumann problem for fully nonlinear parabolic and elliptic equations JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2013 SP - 1109 EP - 1165 VL - 19 IS - 4 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/cocv/2013047/ DO - 10.1051/cocv/2013047 LA - en ID - COCV_2013__19_4_1109_0 ER -
%0 Journal Article %A Daniel, Jean-Paul %T A game interpretation of the Neumann problem for fully nonlinear parabolic and elliptic equations %J ESAIM: Control, Optimisation and Calculus of Variations %D 2013 %P 1109-1165 %V 19 %N 4 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/cocv/2013047/ %R 10.1051/cocv/2013047 %G en %F COCV_2013__19_4_1109_0
Daniel, Jean-Paul. A game interpretation of the Neumann problem for fully nonlinear parabolic and elliptic equations. ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 4, pp. 1109-1165. doi: 10.1051/cocv/2013047
Cité par Sources :