Erratum to: An \(L_{p}\) theory of Stochastic PDEs of Divergence Form on Lipschitz Domains
Erratum to: J Theor Probab
Erratum to: An Lptheory of Stochastic PDEs of Divergence Form on Lipschitz Domains
KyeongHun Kim 0
B KyeongHun Kim
0 Department of Mathematics, Korea University , 1 Anamdong Sungbukgu, Seoul 136701 , South Korea
The purpose of this erratum is to correct the assumptions in Theorem 2.10 of [2] (Kim in J Theor Probab 22:220238, 2009). Theorem 2.10 of [2] should be corrected as follows. The point here is that condition (0.1) below is stronger than the one assumed in [2].
Theorem 0; 1 Let p ∈ [2; ∞) and Assumptions 2; 1; 2; 3; 2; 4; 2; 7 and 2; 8 be satisfied; There exists κ = κ (δ0; p; d; K ) ∈ (0; 1) such that if

60H15 · 35R60
d − 2 + p − κ < θ < d − 2 + p + κ
then for any f ∈ ψ −1H −p,1θ (O, τ ), f i ∈ L p,θ (O, τ ), g ∈ L p,θ (O, τ ) and u0 ∈
U p1,θ (O), Eq. (1.1) with initial data u0 has a unique solution u ∈ H p,θ (O, τ ), and for
1
this solution
In Theorem 2.10 of [2], in place of (0.1), the weaker condition
is assumed.
The error of the proof of [2, Theorem 2.10] occurred because it relied on a result
proved in [3, Theorem 2.1], which is related to nondivergence type SPDE. The result
of [3, Theorem 2.1] is proved for the range of θ satisfying (0.3), but it turns out that
[3, Theorem 2.1] is false unless much stronger restriction on θ is assumed (see [1] for
details).
Theorem 2.1 of [3] is corrected in [1, Theorem 2.12] for θ satisfying (0.1). Thus the
proof of Theorem 2.10 of [2] goes throughout without any change if condition (0.1)
is assumed.
Acknowledgments The author thank Prof. N.V. Krylov for finding the error mentioned above.
1. Kim , K. : A weighted Sobolev space theory of parabolic stochastic PDEs on nonsmooth domains . J. Theor. Probab . 27 , 107  136 ( 2014 )
2. Kim , K. : An L ptheory of stochastic PDEs of divergence form on Lipschitz domains . J. Theor. Probab . 22 , 220  238 ( 2009 )
3. Kim , K. : An L ptheory of SPDEs on Lipschitz domains . Potential Anal . 29 , 303  326 ( 2008 )