Doubling nodal solutions to the Yamabe equation in Rn with maximal rank

Maria Medina, Monica Musso

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17 Citations (SciVal)
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Abstract

We construct a new family of entire solutions to the Yamabe equation −Δu=[Formula presented]|u|[Formula presented]u in D1,2(Rn). If n=3 our solutions have maximal rank, being the first example in odd dimension. Our construction has analogies with the doubling of the equatorial spheres in the construction of minimal surfaces in S3(1).

Original languageEnglish
Pages (from-to)145-188
JournalJournal des Mathematiques Pures et Appliquees
Volume152
Early online date28 May 2021
DOIs
Publication statusPublished - 31 Aug 2021

Bibliographical note

Funding Information:
The first author was partially supported by the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement N 754446 and UGR Research and Knowledge Transfer Found - Athenea3i, and by Project PDI2019-110712GB-100 , MICINN , Spain. The second author is supported by EPSRC Research Grant EP/T008458/1 .

Publisher Copyright:
© 2021 Elsevier Masson SAS

Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.

Keywords

  • Lyapunov-Schmidt reduction
  • Maximal solutions
  • Yamabe problem

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics

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