Abstract In this paper, we prove a variational formula of torsional rigidity under the Orlicz sum, and then introduce the Orlicz mixed torsional rigidity which yields the Orlicz-Brunn-Minkowski inequality and Orlicz-Minkowski inequality for torsional rigidity. As an application, we prove the existence of solution to the Orlicz-Minkowski problem for discrete measure and general measure associated with torsional rigidity.

中文翻译：

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扭转刚度的 Orlicz-Minkowski 问题

摘要 本文证明了Orlicz和下扭转刚度的变分公式，然后引入Orlicz混合扭转刚度，得到扭转刚度的Orlicz-Brunn-Minkowski不等式和Orlicz-Minkowski不等式。作为一个应用，我们证明了离散测度和与扭转刚度相关的一般测度的 Orlicz-Minkowski 问题的解的存在性。