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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm176-3-4,
author = {Djivede Kelome and Andrzej \'Swi\k ech},
title = {Perron's method and the method of relaxed limits for "unbounded" PDE in Hilbert spaces},
journal = {Studia Mathematica},
volume = {173},
year = {2006},
pages = {249-277},
zbl = {1110.49027},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm176-3-4}
}
Djivede Kelome; Andrzej Święch. Perron's method and the method of relaxed limits for "unbounded" PDE in Hilbert spaces. Studia Mathematica, Tome 173 (2006) pp. 249-277. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm176-3-4/