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Stinga","submitted_at":"2017-01-04T16:41:13Z","abstract_excerpt":"For $0<s<1$, we consider the Dirichlet problem for the fractional nonlocal Ornstein--Uhlenbeck equation $$\\begin{cases} (-\\Delta+x\\cdot\\nabla)^su=f&\\hbox{in}~\\Omega\\\\ u=0&\\hbox{on}~\\partial\\Omega, \\end{cases}$$ where $\\Omega$ is a possibly unbounded open subset of $\\mathbb{R}^n$, $n\\geq2$. The appropriate functional settings for this nonlocal equation and its corresponding extension problem are developed. We apply Gaussian symmetrization techniques to derive a concentration comparison estimate for solutions. 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