Perron's method and the method of relaxed limits for
Studia Mathematica, Tome 176 (2006) no. 3, p. 249.

Voir la notice de l'article dans European Digital Mathematics Library

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.
Classification : 35R15, 35J60, 49L20, 49L25
Mots-clés : viscosity solutions, Hamilton-Jacobi-Bellman equations, Perron's method, relaxed limits, Hilbert spaces 
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Djivede Kelome; Andrzej Święch. Perron's method and the method of relaxed limits for. Studia Mathematica, Tome 176 (2006) no. 3, p. 249. https://geodesic-test.mathdoc.fr/item/STUMA_2006__176_3_285275/