Advances in Differential Equations

Non-autonomous Ornstein-Uhlenbeck equations in exterior domains

Tobias Hansel and Abdelaziz Rhandi

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In this paper, we consider non-autonomous Ornstein-Uhlenbeck operators in smooth exterior domains $\Omega\subset \mathbb R^d$ subject to Dirichlet boundary conditions. Under suitable assumptions on the coefficients, the solution of the corresponding non-autonomous parabolic Cauchy problem is governed by an evolution system $\{P_\Omega(t,s)\}_{0\le s\le t}$ on $L^p(\Omega)$ for $1< p < \infty$. Furthermore, $L^p$-estimates for spatial derivatives and $L^p$-$L^q$ smoothing properties of $P_\Omega(t,s),\,0\le s\le t,$ are obtained.

Article information

Adv. Differential Equations, Volume 16, Number 3/4 (2011), 201-220.

First available in Project Euclid: 18 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35B45: A priori estimates 35B65: Smoothness and regularity of solutions 35K10: Second-order parabolic equations


Hansel, Tobias; Rhandi, Abdelaziz. Non-autonomous Ornstein-Uhlenbeck equations in exterior domains. Adv. Differential Equations 16 (2011), no. 3/4, 201--220.

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