On Divergence form SPDEs with Growing Coefficients in W12 Spaces Without Weights

We consider divergence form uniformly parabolic SPDEs with bounded and measurable leading coefficients and possibly growing lower-order coefficients in the deterministic part of the equations. We look for solutions which are summable to the second power with respect to the usual Lebesgue measure along with their first derivatives with respect to the spatial variable.

[1]  Nicolai V. Krylov,et al.  On Divergence Form SPDEs with VMO Coefficients , 2008, SIAM J. Math. Anal..

[2]  A. Rhandi,et al.  $L^p$-regularity for elliptic operators with unbounded coefficients , 2005, Advances in Differential Equations.

[3]  I. Gyöngy,et al.  On stochastic partial differential equations with Unbounded coefficients , 1992 .

[4]  I. Gyöngy.  Stochastic partial differential equations on manifolds,I , 1993 .

[5]  N. Krylov,et al.  Elliptic and Parabolic Second-Order PDEs with Growing Coefficients , 2008, 0806.3100.

[6]  N. Krylov,et al.  Itô’s formula for the Lp-norm of stochastic $${W^{1}_{p}}$$ -valued processes , 2008, 0806.1557.

[7]  Invariant measures and maximal L2 regularity for nonautonomous Ornstein–Uhlenbeck equations , 2008, 0801.3224.

[8]  Piermarco Cannarsa,et al.  Generation of analytic semigroups by elliptic operators with unbounded coefficents , 1987 .

[9]  N. Krylov,et al.  On the Itô–Wentzell formula for distribution-valued processes and related topics , 2011 .

[10]  P. Cannarsa,et al.  Existence and uniqueness results for a non linear stochastic partial differential equation , 1987 .

[11]  B. Farkas,et al.  Maximal regularity for Kolmogorov operators in L2 spaces with respect to invariant measures , 2006 .

[12]  N. V. Krylov.  Filtering equations for partially observable diffusion processes with Lipschitz continuous coefficients , 2009 .

[13]  A. Rhandi,et al.  The domain of the Ornstein-Uhlenbeck operator on an $L^p$-space with invariant measure , 2002 .

[14]  B. Rozovskii,et al.  Stochastic evolution equations , 1981 .

[15]  René Carmona,et al.  Stochastic Partial Differential Equations: Six Perspectives , 1998 .

[16]  G. Cupini,et al.  Maximal regularity in $L^p(\Bbb R^N)$ for a class of elliptic operators with unbounded coefficients , 2004, Differential and Integral Equations.

[17]  A. Rhandi,et al.  THE DOMAIN OF ELLIPTIC OPERATORS ON L(R) WITH UNBOUNDED DRIFT COEFFICIENTS , 2012 .

[18]  Sigurd Assing,et al.  Invariant measures for stochastic heat equations with unbounded coefficients , 2003 .

[19]  Kyeong-Hun Kim.  On Lp-theory of stochastic partial differential equations of divergence form in C1 domains , 2004 .