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

N. V. Krylov; S. V. Lototsky

doi:10.1137/s0036141097326908

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

N. V. Krylov, S. V. Lototsky

School of Mathematics

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

39 Scopus citations

Abstract

Equations of the form du = (au_xx + f_x) dt + Σ_k(σ^ku_x + g^k) dw_t^k 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 language	English (US)
Pages (from-to)	298-325
Number of pages	28
Journal	SIAM Journal on Mathematical Analysis
Volume	30
Issue number	2
DOIs	https://doi.org/10.1137/s0036141097326908
State	Published - 1998

Keywords

Sobolev spaces with weights
Stochastic partial differential equations

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10.1137/s0036141097326908

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abstract = "Equations of the form du = (auxx + fx) dt + Σk(σkux + 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, ∞).",

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AU - Lototsky, S. V.

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AB - Equations of the form du = (auxx + fx) dt + Σk(σkux + 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, ∞).

KW - Sobolev spaces with weights

KW - Stochastic partial differential equations

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

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