A tool for symmetry breaking and multiplicity in some nonlocal problems

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A tool for symmetry breaking and multiplicity in some nonlocal problems. / Musina, Roberta; Nazarov, Alexander I.

In: Mathematical Methods in the Applied Sciences, Vol. 43, No. 16, 15.11.2020, p. 9345-9357.

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

Author

Musina, Roberta ; Nazarov, Alexander I. / A tool for symmetry breaking and multiplicity in some nonlocal problems. In: Mathematical Methods in the Applied Sciences. 2020 ; Vol. 43, No. 16. pp. 9345-9357.

BibTeX

@article{277bce7b5c6648518a9b9b3e7f254d81,

title = "A tool for symmetry breaking and multiplicity in some nonlocal problems",

abstract = "We prove some basic inequalities relating the Gagliardo-Nirenberg seminorms of a symmetric function (Formula presented.) on (Formula presented.) and of its perturbation (Formula presented.), where (Formula presented.) is a suitably chosen eigenfunction of the Laplace-Beltrami operator on the sphere (Formula presented.), thus providing a technical but rather powerful tool to detect symmetry breaking and multiplicity phenomena in variational equations driven by the fractional Laplace operator. A concrete application to a problem related to the fractional Caffarelli-Kohn-Nirenberg inequality is given.",

keywords = "fractional Laplacian, multiplicity, symmetry breaking",

author = "Roberta Musina and Nazarov, {Alexander I.}",

note = "Publisher Copyright: {\textcopyright} 2020 John Wiley & Sons, Ltd.",

year = "2020",

month = nov,

day = "15",

doi = "10.1002/mma.6220",

language = "English",

volume = "43",

pages = "9345--9357",

journal = "Mathematical Methods in the Applied Sciences",

issn = "0170-4214",

publisher = "Wiley-Blackwell",

number = "16",

}

RIS

TY - JOUR

T1 - A tool for symmetry breaking and multiplicity in some nonlocal problems

AU - Musina, Roberta

AU - Nazarov, Alexander I.

PY - 2020/11/15

Y1 - 2020/11/15

N2 - We prove some basic inequalities relating the Gagliardo-Nirenberg seminorms of a symmetric function (Formula presented.) on (Formula presented.) and of its perturbation (Formula presented.), where (Formula presented.) is a suitably chosen eigenfunction of the Laplace-Beltrami operator on the sphere (Formula presented.), thus providing a technical but rather powerful tool to detect symmetry breaking and multiplicity phenomena in variational equations driven by the fractional Laplace operator. A concrete application to a problem related to the fractional Caffarelli-Kohn-Nirenberg inequality is given.

AB - We prove some basic inequalities relating the Gagliardo-Nirenberg seminorms of a symmetric function (Formula presented.) on (Formula presented.) and of its perturbation (Formula presented.), where (Formula presented.) is a suitably chosen eigenfunction of the Laplace-Beltrami operator on the sphere (Formula presented.), thus providing a technical but rather powerful tool to detect symmetry breaking and multiplicity phenomena in variational equations driven by the fractional Laplace operator. A concrete application to a problem related to the fractional Caffarelli-Kohn-Nirenberg inequality is given.

KW - fractional Laplacian

KW - multiplicity

KW - symmetry breaking

UR - http://www.scopus.com/inward/record.url?scp=85079170023&partnerID=8YFLogxK

U2 - 10.1002/mma.6220

DO - 10.1002/mma.6220

M3 - Article

VL - 43

SP - 9345

EP - 9357

JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

SN - 0170-4214

IS - 16

ER -

ID: 78458182