Second Order Partial Differential Equations in Hilbert Spaces: Bibliography

By Giuseppe Da Prato, Jerzy Zabczyk. 2002

339 citations recorded by the source corpus.

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Citations in the corpus

Conservative stochastic Cahn–Hilliard equation with reflection (2006, background): “This process is a gradient system in H0 with nondegenerate noise and with a convex potential Uε(ce0 + ·): the proof of the strong Feller property can be found in [10], Chapter 12.”
Infinite horizon backward stochastic differential equations and elliptic equations in Hilbert spaces (2004, background): “Even in the linear case, such extensions, considered since the works of Gross [17] and Daleckij [5], possess special features and difficulties: see [6, 30] for recent results in the parabolic case, or Chapter 8 in [9].”
Gradient estimates in parabolic problems with unbounded coefficients (2004, unknown): “for all t ≥ 0 and f ∈ Cb(Ω) (for more details see [6]).”
Kolmogorov equations and weak order analysis for SPDEs with nonlinear diffusion coefficient (2017, background): “In the case of an additive noise, it has been the object of several studies, see [11], [16], [17], [34], [44] and the references therein.”
Stochastic optimal control of delay equations arising in advertising models (2004, background): “Barbu and Da Prato [1], Da Prato and Zabczyk [5] and Gozzi [15], [16]).”
On Bayesian A- and D-optimal experimental designs in infinite dimensions (2014, methodology): “In what follows, we shall use the following result, which is a consequence of Proposition 1.2.8 in Da Prato and Zabczyk (2002).”
Strong uniqueness for stochastic evolution equations in Hilbert spaces perturbed by a bounded measurable drift (2011, unknown): “According to [DZ02], for any φ ∈ Bb(H) and any t > 0 one has Rtφ ∈ C∞ b (H) = ∩k≥1C b (H).”