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

Authors
Krylov, NV Lototsky, SV
Citation
Nv. Krylov et Sv. Lototsky, A Sobolev space theory of SPDEs with constant coefficients on a half line, SIAM J MATH, 30(2), 1998, pp. 298-325
Citations number
13
Categorie Soggetti
Mathematics
Journal title
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
ISSN journal
00361410 → ACNP
Volume
30
Issue
2
Year of publication
1998
Pages
298 - 325
Database
ISI
SICI code
0036-1410(19981120)30:2<298:ASSTOS>2.0.ZU;2-9
Abstract
Equations of the form du = (au(xx) + f(x)) dt + Sigma(k) (sigma(k)u(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 positi ve or negative derivatives, summable to the power p is an element of [2, in finity).