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Crandall, M.G. and Lions, P.L. (1983) Viscosity Solutions of Hamilton-Jacobi Equations. Transactions of the American Mathematical Society, 277, 1-42.
https://doi.org/10.1090/S0002-9947-1983-0690039-8

has been cited by the following article:

• TITLE: Stochastic Viscosity Solutions for SPDEs with Discontinuous Coefficients

  AUTHORS: Yidong Zhang

  KEYWORDS: Stochastic Partial Differential Equation, Stochastic Viscosity Solution, Backward Doubly Stochastic Differential Equation

  JOURNAL NAME: Applied Mathematics, Vol.11 No.11, November 30, 2020

  ABSTRACT: In this paper, a class of nonlinear stochastic partial differential equations with discontinuous coefficients is investigated. This study is motivated by some research on stochastic viscosity solutions under non-Lipschitz conditions recently. By studying the solutions of backward doubly stochastic differential equations with discontinuous coefficients and constructing a new approximation function fn to the coefficient f, we get the existence of stochastic viscosity sub-solutions (or super-solutions).The results of this paper can be seen as the extension and application of related articles.