A Sobolev space theory of SPDEs with constant coefficients in a half space

N. V. Krylov, S. V. Lototsky

Research output: Contribution to journalArticlepeer-review

51 Scopus citations

Abstract

Equations of the form du = (aScript i signScript j signScript u signcursive greek chiScript i signcursive greek chiScript j sign + DScript i signScript f signScript i sign) Script d signScript t sign + ΣScript k signScript i signScript k signScript u signcursive greek chiScript i sign + Script g signScript k sign)Script d signScript w signScript k signScript t sign are considered for Script t sign > 0 and cursive greek chi ∈ ℝScript 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 languageEnglish (US)
Pages (from-to)19-33
Number of pages15
JournalSIAM Journal on Mathematical Analysis
Volume31
Issue number1
DOIs
StatePublished - 1999

Keywords

  • Sobolev spaces with weights
  • Stochastic partial differential equations

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