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• W3186117948 abstract "We prove the existence of regular optimal $G$-invariant partitions, with an arbitrary number $ellgeq 2$ of components, for the Yamabe equation on a closed Riemannian manifold $(M,g)$ when $G$ is a compact group of isometries of $M$ with infinite orbits. To this aim, we study a weakly coupled competitive elliptic system of $ell$ equations, related to the Yamabe equation. We show that this system has a least energy $G$-invariant solution with nontrivial components and we show that the limit profiles of the its components separate spatially as the competition parameter goes to $-infty$, giving rise to an optimal partition. For $ell=2$ the optimal partition obtained yields a least energy sign-changing $G$-invariant solution to the Yamabe equation with precisely two nodal domains." @default.
• W3186117948 created "2021-08-02" @default.
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• W3186117948 date "2021-07-22" @default.
• W3186117948 modified "2023-10-03" @default.
• W3186117948 title "Yamabe systems and optimal partitions on manifolds with symmetries" @default.
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