Schauder estimates for stationary and evolution equations associated to stochastic reaction-diffusion equations driven by colored noise. (English) Zbl 1543.35280
Summary: We consider stochastic reaction-diffusion equations with colored noise on the space of real-valued and continuous functions on a compact subset of \(\mathbb{R}^d\) for \(d=1,2,3\). We prove Schauder-type estimates, which will depend on the color of the noise, for the stationary and evolution problems associated with the corresponding transition semigroup.
MSC:
| 35R15 | PDEs on infinite-dimensional (e.g., function) spaces (= PDEs in infinitely many variables) |
| 35R60 | PDEs with randomness, stochastic partial differential equations |
| 47D06 | One-parameter semigroups and linear evolution equations |
| 47D07 | Markov semigroups and applications to diffusion processes |
| 60H30 | Applications of stochastic analysis (to PDEs, etc.) |
Keywords:
colored noise; evolution equations; infinite-dimensional analysis; Schauder estimates; stationary equations; stochastic reaction-diffusion equationsReferences:
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