We prove a cone-type criterion for a boundary point to be regular for the Dirichlet problem related to (possibly) degenerate Ornstein–Uhlenbeck operators in $ \mathbb{R}^N $. Our result extends the classical Zaremba cone criterion for the Laplace operator.

中文翻译：

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次椭圆简并Ornstein-Uhlenbeck算子的Zaremba型准则

我们证明了与（可能）简并的Ornstein-Uhlenbeck算子有关的Dirichlet问题的边界点的锥型准则是规则的，\\ mathbb {R} ^ N $。我们的结果扩展了Laplace算子的经典Zaremba锥准则。