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

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Kelome D., Święch A.

Studia Mathematica

2006

tom 176

nr 3

249-277

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.

Ograniczanie wyników

1 Studia Mathematica

1 Kelome D.

1 Święch A.

1 2006

Wyniki wyszukiwania

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