A Sobolev space theory of SPDEs with constant coefficients on a half line

N. V. Krylov, S. V. Lototsky

Research output: Contribution to journalArticlepeer-review

38 Scopus citations

Abstract

Equations of the form du = (auxx + fx) dt + Σkkux + gk) dwtk are considered for t > 0 and x > 0. The unique solvability of these equations is proved in weighted Sobolev spaces with fractional positive or negative derivatives, summable to the power p ∈ [2, ∞).

Original languageEnglish (US)
Pages (from-to)298-325
Number of pages28
JournalSIAM Journal on Mathematical Analysis
Volume30
Issue number2
DOIs
StatePublished - 1998

Keywords

  • Sobolev spaces with weights
  • Stochastic partial differential equations

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