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- W4306311925 abstract "We show uniqueness in law for the critical SPDE begin{eqnarray} label{qq1} dX_t = AX_t dt + (-A)^{1/2}F(X(t))dt + dW_t,;; X_0 =x in H, end{eqnarray} where $A$ $ : text{dom}(A) subset H to H$ is a negative definite self-adjoint operator on a separable Hilbert space $H$ having $A^{-1}$ of trace class and $W$ is a cylindrical Wiener process on $H$. Here $F: H to H $ can be locally Holder continuous with at most linear growth (some functions $F$ which grow more than linearly can also be considered). This leads to new uniqueness results for generalized stochastic Burgers equations and for three-dimensional stochastic Cahn-Hilliard type equations which have interesting applications. We do not know if uniqueness holds under the sole assumption of continuity of $F$ plus growth condition as stated in [Priola, Ann. of Prob. 49 (2021)]. To get weak uniqueness we use an infinite dimensional localization principle and an optimal regularity result for the Kolmogorov equation $ lambda u - L u = f$ associated to the SPDE when $F = z in H$ is constant and $lambda >0$. This optimal result is similar to a theorem of [Da Prato, J. Evol. Eq. 3 (2003)]." @default.
- W4306311925 created "2022-10-15" @default.
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- W4306311925 date "2022-10-13" @default.
- W4306311925 modified "2023-10-16" @default.
- W4306311925 title "Correction to An optimal regularity result for Kolmogorov equations and weak uniqueness for some critical SPDEs" @default.
- W4306311925 doi "https://doi.org/10.48550/arxiv.2210.07096" @default.
- W4306311925 hasPublicationYear "2022" @default.
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