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

N. V. Krylov

doi:10.1006/jfan.2000.3728

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

N. V. Krylov

Mathematics

Research output: Contribution to journal › Article › peer-review

51 Scopus citations

Abstract

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

Original language	English (US)
Pages (from-to)	1-41
Number of pages	41
Journal	Journal of Functional Analysis
Volume	183
Issue number	1
DOIs	https://doi.org/10.1006/jfan.2000.3728
State	Published - 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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AB - 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.

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

Abstract

Bibliographical note

Keywords

Access

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