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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...

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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
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first_indexed 2019-07-09T21:39:32Z
last_indexed 2020-07-16T19:11:46Z
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spelling 2020-07-16T18:20:28.6178243 v2 51042 2019-07-09 Quantitative symmetry breaking of groundstates for a class of weighted Emden–Fowler equations 46bf09624160610d6d6cf435996a5913 Carlo Mercuri Carlo Mercuri true false 2019-07-09 FGSEN 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. Journal Article Nonlinearity 32 11 4445 4464 IOP Publishing 0951-7715 1361-6544 Symmetry breaking, Liouville theorems, Best constants, Groundstate solutions. 1 11 2019 2019-11-01 10.1088/1361-6544/ab2d6f COLLEGE NANME Science and Engineering - Faculty COLLEGE CODE FGSEN Swansea University 2020-07-16T18:20:28.6178243 2019-07-09T15:44:58.2011486 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Carlo Mercuri 1 Ederson Moreira dos Santos 2 0051042-09072019154541.pdf Last-Version-utf8.pdf 2019-07-09T15:45:41.6800000 Output 461900 application/pdf Accepted Manuscript true 2020-10-09T00:00:00.0000000 true eng
title Quantitative symmetry breaking of groundstates for a class of weighted Emden–Fowler equations
spellingShingle Quantitative symmetry breaking of groundstates for a class of weighted Emden–Fowler equations
Carlo Mercuri
title_short Quantitative symmetry breaking of groundstates for a class of weighted Emden–Fowler equations
title_full Quantitative symmetry breaking of groundstates for a class of weighted Emden–Fowler equations
title_fullStr Quantitative symmetry breaking of groundstates for a class of weighted Emden–Fowler equations
title_full_unstemmed Quantitative symmetry breaking of groundstates for a class of weighted Emden–Fowler equations
title_sort Quantitative symmetry breaking of groundstates for a class of weighted Emden–Fowler equations
author_id_str_mv 46bf09624160610d6d6cf435996a5913
author_id_fullname_str_mv 46bf09624160610d6d6cf435996a5913_***_Carlo Mercuri
author Carlo Mercuri
author2 Carlo Mercuri
Ederson Moreira dos Santos
format Journal article
container_title Nonlinearity
container_volume 32
container_issue 11
container_start_page 4445
publishDate 2019
institution Swansea University
issn 0951-7715
1361-6544
doi_str_mv 10.1088/1361-6544/ab2d6f
publisher IOP Publishing
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
document_store_str 1
active_str 0
description 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.
published_date 2019-11-01T04:02:47Z
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score 11.016235

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