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arXiv · 1910.07101

Phase separation, optimal partitions, and nodal solutions to the Yamabe equation on the sphere

Mónica Clapp·Alberto Saldaña·Andrzej Szulkin
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Abstract

We study an optimal M-partition problem for the Yamabe equation on the round sphere, in the presence of some particular symmetries. We show that there is a correspondence between solutions to this problem and least-energy sign-changing symmetric solutions to the Yamabe equation on the sphere with precisely M nodal domains. The existence of an optimal partition is established through the study of the limit profiles of least-energy solutions to a weakly coupled competitive elliptic system on the sphere.

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Mónica Clapp, Alberto Saldaña, Andrzej Szulkin. 2019-10-15. Phase separation, optimal partitions, and nodal solutions to the Yamabe equation on the sphere. https://arxiv.org/abs/1910.07101

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