TY - JOUR

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

AU - Musina, Roberta

AU - Nazarov, Alexander I.

N1 - Publisher Copyright: © 2020 John Wiley & Sons, Ltd.

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 -