Journal article 772 views 110 downloads
Quantitative symmetry breaking of groundstates for a class of weighted Emden–Fowler equations
Carlo Mercuri,
Ederson Moreira dos Santos
Nonlinearity, Volume: 32, Issue: 11, Pages: 4445 - 4464
Swansea University Author: Carlo Mercuri
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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...
| Published in: | Nonlinearity |
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| ISSN: | 0951-7715 1361-6544 |
| Published: |
IOP Publishing
2019
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| Online Access: |
Check full text
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa51042 |
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| 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. |
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| Keywords: |
Symmetry breaking, Liouville theorems, Best constants, Groundstate solutions. |
| College: |
Faculty of Science and Engineering |
| Issue: |
11 |
| Start Page: |
4445 |
| End Page: |
4464 |