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References

  1. Flandoli, Franco. Dirichlet boundary value problem for stochastic parabolic equations: compatibility relations and regularity of solutions. Stochastics Stochastics Rep. 29 (1990), no. 3, 331--357. MR1042066 (91c:35169)
  2. Flandoli, Franco. An introduction to 3D stochastic fluid dynamics. SPDE in hydrodynamic: recent progress and prospects, 51--150, Lecture Notes in Math., 1942, Springer, Berlin, 2008. MR2459085 (2009j:76191)
  3. T. Funaki, Random motion of strings and related stochastic evolution equations, Nagoya Math. J. 89 (1983), 129--193.
  4. Gilbarg, David; Hörmander, Lars. Intermediate Schauder estimates. Arch. Rational Mech. Anal. 74 (1980), no. 4, 297--318. MR0588031 (82a:35038)
  5. Kim, Kyeong-Hun. On $Lsb p$-theory of stochastic partial differential equations of divergence form in $Csp 1$ domains. Probab. Theory Related Fields 130 (2004), no. 4, 473--492. MR2102888 (2005h:60185)
  6. Kim, Kyeong-Hun. On stochastic partial differential equations with variable coefficients in $Csp 1$ domains. Stochastic Process. Appl. 112 (2004), no. 2, 261--283. MR2073414 (2005e:60128)
  7. K. Kim, $L_p$ estimates for SPDE with discontinuous coefficients in domains/}, Electronic Journal of Probability, 10 (2005), no. 1, 1-20.
  8. K. Lee and K. Kim, A $W^n_2$-Theory of Stochastic Partial Differential Systems of Non-divergent type on $C^1$ domains, preprint.
  9. Kim, Kyeong-Hun; Krylov, N. V. On SPDEs with variable coefficients in one space dimension. Potential Anal. 21 (2004), no. 3, 209--239. MR2075669 (2005i:60120)
  10. Kim, Kyeong-Hun; Krylov, N. V. On the Sobolev space theory of parabolic and elliptic equations in $Csp 1$ domains. SIAM J. Math. Anal. 36 (2004), no. 2, 618--642. MR2111792 (2005k:35168)
  11. N.V. Krylov, Ito's formula for the $L_p$-norm of stochastic $W^1_p$-valued processes. Probab. Theory Related Fields 147 (2010), no. 3-4, 583-605.
  12. Krylov, N. V. Some properties of traces for stochastic and deterministic parabolic weighted Sobolev spaces. J. Funct. Anal. 183 (2001), no. 1, 1--41. MR1837532 (2002c:46069)
  13. Krylov, N. V. An analytic approach to SPDEs. Stochastic partial differential equations: six perspectives, 185--242, Math. Surveys Monogr., 64, Amer. Math. Soc., Providence, RI, 1999. MR1661766 (99j:60093)
  14. Krylov, N. V. Weighted Sobolev spaces and Laplace's equation and the heat equations in a half space. Comm. Partial Differential Equations 24 (1999), no. 9-10, 1611--1653. MR1708104 (2000j:46065)
  15. Krylov, N. V.; Lototsky, S. V. A Sobolev space theory of SPDEs with constant coefficients in a half space. SIAM J. Math. Anal. 31 (1999), no. 1, 19--33 (electronic). MR1720129 (2001a:60072)
  16. Lototsky, S. V. Sobolev spaces with weights in domains and boundary value problems for degenerate elliptic equations. Methods Appl. Anal. 7 (2000), no. 1, 195--204. MR1796011 (2001m:46077)
  17. Mikulevicius, R. On strong $Hsb 2sp 1$-solutions of stochastic Navier-Stokes equation in a bounded domain. SIAM J. Math. Anal. 41 (2009), no. 3, 1206--1230. MR2529962 (2011a:60232)
  18. Mikulevicius, R. On the Cauchy problem for stochastic Stokes equations. SIAM J. Math. Anal. 34 (2002), no. 1, 121--141 (electronic). MR1950829 (2003k:60154)
  19. Mikulevicius, R.; Rozovskii, B. L. Global $Lsb 2$-solutions of stochastic Navier-Stokes equations. Ann. Probab. 33 (2005), no. 1, 137--176. MR2118862 (2005k:60198)
  20. Mikulevicius, R.; Rozovskii, B. A note on Krylov's $Lsb p$-theory for systems of SPDEs. Electron. J. Probab. 6 (2001), no. 12, 35 pp. (electronic). MR1831807 (2003a:60097)
  21. Mueller, C.; Tribe, R. Hitting properties of a random string. Electron. J. Probab. 7 (2002), no. 10, 29 pp. (electronic). MR1902843 (2003g:60111)
  22. Pardoux, E. Stochastic partial differential equations and filtering of diffusion processes. Stochastics 3, no. 2, 127--167. (1979), MR0553909 (81b:60059)
  23. Rozovskiĭ, B. L. Stochastic evolution systems.Linear theory and applications to nonlinear filtering.Translated from the Russian by A. Yarkho.Mathematics and its Applications (Soviet Series), 35. Kluwer Academic Publishers Group, Dordrecht, 1990. xviii+315 pp. ISBN: 0-7923-0037-8 MR1135324 (92k:60136)
  24. Yoo, Hyek. $Lsb p$-estimates for stochastic PDEs with discontinuous coefficients. Stochastic Anal. Appl. 17 (1999), no. 4, 687--711. MR1693563 (2000f:60093)
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