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Pré-Publication, Document De Travail Année : 2018

Smoothing Properties of Fractional Ornstein-Uhlenbeck Semigroups and Null-Controllability

Paul Alphonse
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Joackim Bernier

Résumé

We study fractional hypoelliptic Ornstein-Uhlenbeck operators acting on $L^2(\mathbb{R}^n)$ satisfying the Kalman rank condition. We prove that the semigroups generated by these operators enjoy Gevrey regularizing effects. Two byproducts are derived from this smoothing property. On the one hand, we prove the null-controllability in any positive time from thick control subsets of the associated parabolic equations posed on the whole space. On the other hand, by using the interpolation theory, we get global $L^2$ subelliptic estimates for the these operators.
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Dates et versions

hal-01888835 , version 1 (05-10-2018)
hal-01888835 , version 2 (07-07-2020)

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Paul Alphonse, Joackim Bernier. Smoothing Properties of Fractional Ornstein-Uhlenbeck Semigroups and Null-Controllability. 2018. ⟨hal-01888835v1⟩
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