Some Properties of Traces for Stochastic and Deterministic Parabolic Weighted Sobolev Spaces

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Abstract

The results presented provide information on the behavior near x1=0 for fixed t>0 in the sense of Lp-spaces with weights for functions u(t)=u(t, x1, x′) (x1≥0, x′∈Rd-1, t≥0) satisfying stochastic partial differential equations of type du(t)=(Δu(t)+f(t))dt+gk(t)dwkt with zero boundary condition on x1=0.

Original languageEnglish (US)
Pages (from-to)1-41
Number of pages41
JournalJournal of Functional Analysis
Volume183
Issue number1
DOIs
StatePublished - Jun 20 2001

Bibliographical note

Funding Information:
1The work was partially supported by NSF Grant DMS-9876586.

Keywords

  • Embedding theorems; Sobolev spaces with weights

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