## Abstract

Equations of the form du = (a^{Script i signScript j sign}Script u sign_{cursive greek chiScript i signcursive greek chiScript j sign} + D_{Script i sign}Script f sign^{Script i sign}) Script d signScript t sign + Σ_{Script k sign}(σ^{Script i signScript k sign}Script u sign_{cursive greek chiScript i sign} + Script g sign^{Script k sign})Script d signScript w sign^{Script k sign}_{Script t sign} are considered for Script t sign > 0 and cursive greek chi ∈ ℝ^{Script d sign}_{+}. The unique solvability of these equations is proved in weighted Sobolev spaces with fractional positive or negative derivatives, summable to the power Script p sign ∈ (2, ∞).

Original language | English (US) |
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Pages (from-to) | 19-33 |

Number of pages | 15 |

Journal | SIAM Journal on Mathematical Analysis |

Volume | 31 |

Issue number | 1 |

DOIs | |

State | Published - 1999 |

## Keywords

- Sobolev spaces with weights
- Stochastic partial differential equations