A Sobolev space theory of SPDEs with constant coefficients in a half space

Authors
Krylov, NV Lototsky, SV
Citation
Nv. Krylov et Sv. Lototsky, A Sobolev space theory of SPDEs with constant coefficients in a half space, SIAM J MATH, 31(1), 1999, pp. 19-33
Citations number
9
Categorie Soggetti
Mathematics
Journal title
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
ISSN journal
00361410 → ACNP
Volume
31
Issue
1
Year of publication
1999
Pages
19 - 33
Database
ISI
SICI code
0036-1410(199912)31:1<19:ASSTOS>2.0.ZU;2-D
Abstract
Equations of the form du = (a(ij)u(xixj) +D(i)f(i)) dt + Sigma(k) (sigma(ik )u(xi) + g(k)) dw(t)(k) are considered for t > 0 and x is an element of R-(d). The unique solvability of these equations is proved in weighted Sobole v spaces with fractional positive or negative derivatives, summable to the power p is an element of [2, infinity).