论文标题
一般Riesz型问题的最小化器
Minimisers of a general Riesz-type Problem
论文作者
论文摘要
我们考虑在$ \ Mathbb r^n $中设置的设置，这些设置最小化，对于固定音量，周长和非本地术语的总和，由kernel $ g的双重整合给出：\ mathbb r^n \ setMinus \ {0 \ \} \ to \ mathb r r^+$。我们为最小化者建立了一些一般存在和规律性的结果。在二维情况下，我们表明，如果外围为主的政权，球是一个独特的最小值，对于$ g $的功能范围很广。
We consider sets in $\mathbb R^N$ which minimise, for fixed volume, the sum of the perimeter and a non-local term given by the double integral of a kernel $g:\mathbb R^N\setminus\{0\}\to \mathbb R^+$. We establish some general existence and regularity results for minimisers. In the two-dimensional case we show that balls are the unique minimisers if the perimeter-dominated regime, for a wide class of functions $g$.
