圆形径向狭缝域的Mityuk函数和半径的数值计算
Numerical computation of Mityuk's function and radius for circular-radial slit domains
摘要：
我们考虑了在\cite{Mit}中提出的Mityuk函数和半径，将约化模和共形半径推广到多连通域的情形。本文提出了一种数值方法来计算由具有圆形/径向狭缝的单位圆盘组成的正则域的Mityuk函数和半径。我们的方法是基于边界积分方程与广义Neumann核。特别注意的临界点的存在性和Mityuk的半径的边界表现的理论结果的验证。
英文摘要：
We consider Mityuk's function and radius which have been proposed in \cite{Mit} as generalizations of the reduced modulus and conformal radius to the cases of multiply connected domains. We present a numerical method to compute Mityuk's function and radius for canonical domains that consist of the unit disk with circular/radial slits. Our method is based on the boundary integral equation with the generalized Neumann kernel. Special attention is given to the validation of the theoretical results on the existence of critical points and the boundary behavior of Mityuk's radius.
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