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Quantitative symmetry breaking of groundstates for a class of weighted Emden–Fowler equations

Carlo Mercuri Orcid Logo, Ederson Moreira dos Santos

Nonlinearity, Volume: 32, Issue: 11, Pages: 4445 - 4464

Swansea University Author: Carlo Mercuri Orcid Logo

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DOI (Published version): 10.1088/1361-6544/ab2d6f

Abstract

We prove that symmetrybreaking occurs in dimensions N ≥ 3 for the groundstate solutions to a class of Emden-Fowler equa-tions on the unit ball, with Dirichlet boundary conditions. We show that this phenomenon occurs forlarge values of a certain exponent for a radial weight function appearing in the...

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Published in: Nonlinearity
ISSN: 0951-7715 1361-6544
Published: IOP Publishing 2019
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URI: https://cronfa.swan.ac.uk/Record/cronfa51042
Abstract: We prove that symmetrybreaking occurs in dimensions N ≥ 3 for the groundstate solutions to a class of Emden-Fowler equa-tions on the unit ball, with Dirichlet boundary conditions. We show that this phenomenon occurs forlarge values of a certain exponent for a radial weight function appearing in the equation. The problemreads as a possibly large perturbation of the classical H ́enon equation. In particular we consider aweight function having a spherical shell of zeroes centred at the origin and of radius R. A quantitativecondition on R for this phenomenon to occur is given by means of universal constants, such as thebest constant for the subcritical Sobolev embedding.
Keywords: Symmetry breaking, Liouville theorems, Best constants, Groundstate solutions.
College: Faculty of Science and Engineering
Issue: 11
Start Page: 4445
End Page: 4464

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