The existence of minimizers for an isoperimetric problem with Wasserstein penalty term in unbounded domains

Qinglan Xia, Bohan Zhou

In this article, we consider the (double) minimization problem $$\min\left\{P(E;Ω)+λW_p(E,F):~E\subseteqΩ,~F\subseteq \mathbb{R}^d,~\lvert E\cap F\rvert=0,~ \lvert E\rvert=\lvert F…