Perron's method and the method of relaxed limits for "unbounded" PDE in Hilbert spaces

Djivede Kelome, and Andrzej Święch. "Perron's method and the method of relaxed limits for "unbounded" PDE in Hilbert spaces." Studia Mathematica 176.3 (2006): 249-277. <http://eudml.org/doc/285275>.

@article{DjivedeKelome2006,
abstract = {We prove that Perron's method and the method of half-relaxed limits of Barles-Perthame works for the so called B-continuous viscosity solutions of a large class of fully nonlinear unbounded partial differential equations in Hilbert spaces. Perron's method extends the existence of B-continuous viscosity solutions to many new equations that are not of Bellman type. The method of half-relaxed limits allows limiting operations with viscosity solutions without any a priori estimates. Possible applications of the method of half-relaxed limits to large deviations, singular perturbation problems, and convergence of finite-dimensional approximations are discussed.},
author = {Djivede Kelome, Andrzej Święch},
journal = {Studia Mathematica},
keywords = {viscosity solutions; Hamilton-Jacobi-Bellman equations; Perron's method; relaxed limits; Hilbert spaces},
language = {eng},
number = {3},
pages = {249-277},
title = {Perron's method and the method of relaxed limits for "unbounded" PDE in Hilbert spaces},
url = {http://eudml.org/doc/285275},
volume = {176},
year = {2006},
}

TY - JOUR
AU - Djivede Kelome
AU - Andrzej Święch
TI - Perron's method and the method of relaxed limits for "unbounded" PDE in Hilbert spaces
JO - Studia Mathematica
PY - 2006
VL - 176
IS - 3
SP - 249
EP - 277
AB - We prove that Perron's method and the method of half-relaxed limits of Barles-Perthame works for the so called B-continuous viscosity solutions of a large class of fully nonlinear unbounded partial differential equations in Hilbert spaces. Perron's method extends the existence of B-continuous viscosity solutions to many new equations that are not of Bellman type. The method of half-relaxed limits allows limiting operations with viscosity solutions without any a priori estimates. Possible applications of the method of half-relaxed limits to large deviations, singular perturbation problems, and convergence of finite-dimensional approximations are discussed.
LA - eng
KW - viscosity solutions; Hamilton-Jacobi-Bellman equations; Perron's method; relaxed limits; Hilbert spaces
UR - http://eudml.org/doc/285275
ER -