A Sobolev space theory of SPDEs with constant coefficients in a half space. (English) Zbl 0943.60047

Summary: Equations of the form \[ du=(a^{ij}u_{x^{i}x^{j}} +D_{i}f^{i}) dt+\sum_{k}(\sigma^{ik}u_{x^{i}} +g^{k}) dw^{k}_{t} \] are considered for \(t > 0\) and \(x\in\mathbb{R}^{d}_{+}\). The unique solvability of these equations is proved in weighted Sobolev spaces with fractional positive or negative derivatives, summable to the power \(p\in[2,\infty)\).


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