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.

A tool for symmetry breaking and multiplicity in some nonlocal problems

Roberta Musina;
2020-01-01

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11390/1174376
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