On divergence form SPDEs with growing coefficients in W1 2 spaces without weights

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Abstract

We consider divergence form uniformly parabolic stochastic partial differential equations with bounded and measurable leading coefficients and possibly growing lower-order coefficients in the deterministic part of the equations. We look for solutions which are summable to the second power with respect to the usual Lebesgue measure along with their first derivatives with respect to the spatial variable.

Original languageEnglish (US)
Pages (from-to)609-633
Number of pages25
JournalSIAM Journal on Mathematical Analysis
Volume42
Issue number2
DOIs
StatePublished - May 14 2010

Keywords

  • Divergence-type equations
  • Growing coefficients
  • Sobolev-hilbert spaces without weights
  • Stochastic partial differential equations

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