Optimal pinwheel partitions for the Yamabe equation (Q6601327)

The authors obtain the existence of a solution for a weakly coupled competitive Yamabe system whose components are invariant under the action of the group. Then, observing that the components of the solutions segregate, they deduce the existence of an optimal partition for the Yamabe equation in \(\mathbb{R}^n\) consisting of mutually linearly isometric sets, each invariant under the action of a group of linear isometries. Moreover, the existence of new infinitely many sign-changing solutions for the Yamabe equation in \(\mathbb{R}^n\) is also obtained.