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Uniqueness of weak solutions of fully nonlinear stochastic partial differential equations. (English. Abridged French version) Zbl 0970.60072
It is given a uniqueness result for stochastic viscosity solutions of fully nonlinear second-order stochastic partial differential equations where the diffusion part is depending only on the gradient of the unknown scalar function. This note is an extension of the new theory, introduced by the same authors, and it is based on expressing the solution of the stochastic part using the method of characteristics. The explanations are given in detail and it is recommended to those working in the field of partial differential equations with stochastic perturbations.

MSC:
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
35R60 PDEs with randomness, stochastic partial differential equations
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
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