We present a quantitative estimate for the radially symmetric configuration concerning a Serrin-type overdetermined problem for the torsional rigidity in a bounded domain $\Omega \subset {\mathbb{R}}^N$, when the equation is known on $\Omega \setminus \overline{\omega }$ only, for some open subset $\omega ⋐\Omega$.

The problem has concrete motivations in optimal heating with malfunctioning, laminar flows and beams with small inhomogeneities.

中文翻译：

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具有部分领域知识的Serrin型问题

我们提出了有关Serrin型超界问题的径向对称构型的定量估计，该问题是有界域中的扭转刚度 $\Omega \subset {\mathbb{[R}}^{ñ}$，当方程在 $\Omega \setminus \overline{\omega }$ 仅对于某些开放子集 $\omega ⋐\Omega$。

该问题的具体动机是在出现故障，层流和不均匀性较小的梁时进行最佳加热。