2019
Том 71
№ 8

# Regularity results for Kolmogorov equations in $L^2 (H, μ)$ spaces and applications

Da Prato G.

Abstract

We consider the transition semigroup $R_t =e^{tsA}$ associated to an Ornstein—Uhlenbeck process in a Hilbert space $H$. We characterize, under suitable assumptions, the domain of $A$ as a subspace $W^{2,2} (H, μ)$, where $μ$ is the invariant measure associated to $R_t$. This characterization is then used to treat some Kolmogorov equations with variable coefficients.

English version (Springer): Ukrainian Mathematical Journal 49 (1997), no. 3, pp 494-505.

Citation Example: Da Prato G. Regularity results for Kolmogorov equations in $L^2 (H, μ)$ spaces and applications // Ukr. Mat. Zh. - 1997. - 49, № 3. - pp. 448–457.

Full text