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Invariance of subspaces under the solution flow of SPDE. (English) Zbl 1210.60067
The author derives some regularity property for the solution to a SPDE, namely that under certain assumptions on the coefficients of the equation, the author proves that the solution takes value in some subspace of the original space if the initial condition does so. This result is stated in Theorem 1.1 in the form of a moment inequality where the norm of the solution process (in an appropriate space) is estimated by the norm of the initial condition plus the one of a quantity related to the coefficients of the equation. As an application, the authors presents in Section 3 several examples of SPDEs which satisfy this general criteria including stochastic reaction-diffusion equations, stochastic porous media and fast diffusion equations and stochastic \(p\)-Laplace equation.

MSC:
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
35R60 PDEs with randomness, stochastic partial differential equations
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