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Phase separation, optimal partitions and nodal solutions to the Yamabe equation on the sphere
Stockholm University, Faculty of Science, Department of Mathematics.
(English)Manuscript (preprint) (Other academic)
Abstract [en]

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.

Keywords [en]
Phase separation, optimal partitions and nodal solutions to the Yamabe equation on the sphere
National Category
Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-175358OAI: oai:DiVA.org:su-175358DiVA, id: diva2:1362754
Available from: 2019-10-21 Created: 2019-10-21 Last updated: 2019-10-22

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arXiv:1910.07101

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CiteExportLink to record
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