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

• Autorzy: Djivede Kelome , Andrzej Święch
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 49L25: Viscosity solutions
• 35R15: Partial differential equations on infinite-dimensional (e.g. function) spaces (= PDE in infinitely many variables)
• 35J60: Nonlinear elliptic equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2006
• Tom: 176
• Numer: 3
• Strony: 249-277

Daty

wydano

2006

Twórcy

autor

Djivede Kelome

• Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003, U.S.A.
• Department of Mathematics and Statistics, McGill University, 805 Sherbrooke St West, Montreal, QC, Canada H3A-2K6

autor

Andrzej Święch

• School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, U.S.A.

Identyfikatory

DOI

10.4064/sm176-3-4