A tool for symmetry breaking and multiplicity in some nonlocal problems

We prove some basic inequalities relating the Gagliardo‐Nirenberg seminorms of a symmetric function u on Rn and of its perturbation uφμ, where φμ is a suitably chosen eigenfunction of the Laplace‐Beltrami operator on the sphere Sn−1, thus providing a technical but rather powerful tool to detect symm...

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Veröffentlicht in:	Mathematical methods in the applied sciences 2020-11, Vol.43 (16), p.9345-9357
Hauptverfasser:	Musina, Roberta, Nazarov, Alexander I.
Format:	Artikel
Sprache:	eng
Schlagworte:	Broken symmetry Eigenvectors fractional Laplacian multiplicity Perturbation Symmetry symmetry breaking Symmetry detection
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