Non-autonomous Ornstein-Uhlenbeck equations in exterior domains

2010/04/18 by Tobias Hansel, Hansel, Tobias, Abdelaziz Rhandi +1
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1004.3013

16 pages

arxiv created 2010/04/18 · arxiv updated 2010/04/20

Abstract

In this paper, we consider non-autonomous Ornstein-Uhlenbeck operators in smooth exterior domains Ω⊂ \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_Ω(t,s)\_{0≤ s≤ t} on L^p(Ω) for 1< p < ∞. Furthermore, L^p-estimates for spatial derivatives and L^p-L^q smoothing properties of P_Ω(t,s), 0≤ s≤ t, are obtained.

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