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

2018/10/05 by Paul Alphonse, Alphonse, Paul, Joackim Berniér +1 · 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

paper · pdf · doi:10.48550/arxiv.1810.02629

openalex publication_date 2018/10/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study fractional hypoelliptic Ornstein-Uhlenbeck operators acting on\nL²(\ℝⁿ) satisfying the Kalman rank condition. We prove that the\nsemigroups generated by these operators enjoy Gevrey regularizing effects. Two\nbyproducts are derived from this smoothing property. On the one hand, we prove\nthe null-controllability in any positive time from thick control subsets of the\nassociated parabolic equations posed on the whole space. On the other hand, by\nusing interpolation theory, we get global L² subelliptic estimates for the\nthese operators.\n

Citations

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

Cited by

• Logarithmic convexity of evolution equations and application to inverse problems

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