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Abstract
In this paper, lower bound of exponential type for the distortion of the transfinite diameter of the image of a disk under regular homeomorphisms belonging to the Sobolev class $W_{\rm loc }^{1,1}$ and possessing the N-property (in the sense of Luzin) is obtained. Moreover, the problem of minimizing the distortion functional of the transfinite diameter of the image of a disk in a certain class of such mappings is solved.
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