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

2018/10/05 by Paul Alphonse, Alphonse, Paul, Joackim Berniér +2 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Stability and Controllability of Differential Equations #math.AP

paper · pdf · doi:10.48550/arxiv.1810.02629

openalex publication_date 2018/10/05 · arxiv created 2020/07/08 · arxiv updated 2020/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study fractional hypoelliptic Ornstein-Uhlenbeck operators acting on L²(ℝⁿ) 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 interpolation theory, we get global L² subelliptic estimates for the these operators.

Citations

• Zufallige Bewegungen (Zur Theorie der Brownschen Bewegung)
• Short-time asymptotics of the regularizing effect for semigroups generated by quadratic operators

Cited by

• Logarithmic convexity of evolution equations and application to inverse problems

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