In this paper, we consider a heat equation with mixed boundary conditions in a two-dimensional domain with a reentrant corner. This allows the solution to exhibit singularities near the corner as well as at the points where the mixed boundary conditions meet. The aim of this work is to establish a Carleman inequality by constructing a convenient weight function. As a consequence, we prove some control results.

中文翻译：

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存在奇异性和可控制性后果时热方程的一个新的Carleman不等式

在本文中，我们考虑了带有折角的二维域中具有混合边界条件的热方程。这使解决方案在拐角处以及混合边界条件满足的点处都显示出奇异性。这项工作的目的是通过构造一个方便的权函数来建立一个卡尔曼不等式。结果，我们证明了一些控制结果。