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Viscosity solutions of fully nonlinear second-order equations and optimal stochastic control in infinite dimensions. III. Uniqueness of viscosity solutions for general second-order equations

Lions, Pierre-Louis (1989), Viscosity solutions of fully nonlinear second-order equations and optimal stochastic control in infinite dimensions. III. Uniqueness of viscosity solutions for general second-order equations, Journal of Functional Analysis, 86, 1, p. 1-18. http://dx.doi.org/10.1016/0022-1236(89)90062-1

Type
Article accepté pour publication ou publié
Date
1989
Journal name
Journal of Functional Analysis
Volume
86
Number
1
Publisher
Elsevier
Pages
1-18
Publication identifier
Metadata
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Author(s)
Lions, Pierre-Louis
Abstract (EN)
We prove here the uniqueness and existence of viscosity solutions for a general class of fully nonlinear second-order equations in an infinite-dimensional Hilbert space. The uniqueness is proved using the so-called inf and sup convolutions which allow some reduction to finite-dimensional problems.
Subjects / Keywords
second-order equations