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

Maria Medina; Monica Musso

doi:10.1016/j.matpur.2021.05.011

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

Maria Medina, Monica Musso

Department of Mathematical Sciences

Universidad Autónoma de Madrid

Research output: Contribution to journal › Article › peer-review

19 Citations (SciVal)

76 Downloads (Pure)

Abstract

We construct a new family of entire solutions to the Yamabe equation −Δu=[Formula presented]|u|^{[Formula presented]}u in D^1,2(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 language	English
Pages (from-to)	145-188
Journal	Journal des Mathematiques Pures et Appliquees
Volume	152
Early online date	28 May 2021
DOIs	https://doi.org/10.1016/j.matpur.2021.05.011
Publication status	Published - 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.

Funding

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 .

Keywords

Lyapunov-Schmidt reduction
Maximal solutions
Yamabe problem

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

Access to Document

10.1016/j.matpur.2021.05.011Licence: Unspecified

Medina-Musso_FinalVersionLicence: Unspecified

Cite this

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title = "Doubling nodal solutions to the Yamabe equation in Rn with maximal rank",

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).",

keywords = "Lyapunov-Schmidt reduction, Maximal solutions, Yamabe problem",

author = "Maria Medina and Monica Musso",

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: {\textcopyright} 2021 Elsevier Masson SAS Copyright: Copyright 2021 Elsevier B.V., All rights reserved.",

year = "2021",

month = aug,

day = "31",

doi = "10.1016/j.matpur.2021.05.011",

language = "English",

volume = "152",

pages = "145--188",

journal = "Journal des Mathematiques Pures et Appliquees",

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T1 - Doubling nodal solutions to the Yamabe equation in Rn with maximal rank

AU - Medina, Maria

AU - Musso, Monica

N1 - 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.

PY - 2021/8/31

Y1 - 2021/8/31

N2 - 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).

AB - 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).

KW - Lyapunov-Schmidt reduction

KW - Maximal solutions

KW - Yamabe problem

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U2 - 10.1016/j.matpur.2021.05.011

DO - 10.1016/j.matpur.2021.05.011

M3 - Article

AN - SCOPUS:85107807555

SN - 0021-7824

VL - 152

SP - 145

EP - 188

JO - Journal des Mathematiques Pures et Appliquees

JF - Journal des Mathematiques Pures et Appliquees

ER -

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

Abstract

Bibliographical note

Funding

Keywords

ASJC Scopus subject areas

Access to Document

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Concentration phenomena in nonlinear analysis

Cite this

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

Abstract

Bibliographical note

Funding

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Projects

Concentration phenomena in nonlinear analysis

Cite this

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