Shape of extremal functions for weighted Sobolev-type inequalities

Shape of extremal functions for weighted Sobolev-type inequalities

We study the shape of solutions to some variational problems in Sobolev spaces with weights that are powers of |x|. In particular, we detect situations when the extremal functions lack symmetry properties such as radial symmetry and antisymmetry. We also prove an isoperimetric inequality for the fir...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Hauptverfasser: Brock, Friedemann, Chiacchio, Francesco, Croce, Gisella, Mercaldo, Anna
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics - Optimization and Control
Online-Zugang:Volltext bestellen
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page
container_issue
container_start_page
container_title
container_volume
creator Brock, Friedemann
Chiacchio, Francesco
Croce, Gisella
Mercaldo, Anna
description We study the shape of solutions to some variational problems in Sobolev spaces with weights that are powers of |x|. In particular, we detect situations when the extremal functions lack symmetry properties such as radial symmetry and antisymmetry. We also prove an isoperimetric inequality for the first non-zero eigenvalue of a weighted Neumann problem.
doi_str_mv 10.48550/arxiv.2311.01083
format Article
fullrecord <record><control><sourceid>arxiv_GOX</sourceid><recordid>TN_cdi_arxiv_primary_2311_01083</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2311_01083</sourcerecordid><originalsourceid>FETCH-LOGICAL-a673-7f23ab8194e0735b9629139d71dc0edcac02fdcfc5f3d4a5f24b299f618d151a3</originalsourceid><addsrcrecordid>eNotz71OwzAUhmEvDKhwAUz4BhL8EyfxCBUUpEoM7R6d2OdQS2lcHPfv7oHS6VtefdLD2IMUZdUaI54gncKhVFrKUkjR6lv2strADnkkjqeccAsDp_3ocojjxCkmfsTwtcno-Sr2ccBDkc-_fRjxew9DyAGnO3ZDMEx4f90ZW7-9rufvxfJz8TF_XhZQN7poSGnoW2krFI02va2Vldr6Rnon0DtwQpF35AxpX4EhVfXKWqpl66WRoGfs8f_2guh2KWwhnbs_THfB6B8ZT0Vd</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Shape of extremal functions for weighted Sobolev-type inequalities</title><source>arXiv.org</source><creator>Brock, Friedemann ; Chiacchio, Francesco ; Croce, Gisella ; Mercaldo, Anna</creator><creatorcontrib>Brock, Friedemann ; Chiacchio, Francesco ; Croce, Gisella ; Mercaldo, Anna</creatorcontrib><description>We study the shape of solutions to some variational problems in Sobolev spaces with weights that are powers of |x|. In particular, we detect situations when the extremal functions lack symmetry properties such as radial symmetry and antisymmetry. We also prove an isoperimetric inequality for the first non-zero eigenvalue of a weighted Neumann problem.</description><identifier>DOI: 10.48550/arxiv.2311.01083</identifier><language>eng</language><subject>Mathematics - Optimization and Control</subject><creationdate>2023-11</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,776,881</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2311.01083$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2311.01083$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Brock, Friedemann</creatorcontrib><creatorcontrib>Chiacchio, Francesco</creatorcontrib><creatorcontrib>Croce, Gisella</creatorcontrib><creatorcontrib>Mercaldo, Anna</creatorcontrib><title>Shape of extremal functions for weighted Sobolev-type inequalities</title><description>We study the shape of solutions to some variational problems in Sobolev spaces with weights that are powers of |x|. In particular, we detect situations when the extremal functions lack symmetry properties such as radial symmetry and antisymmetry. We also prove an isoperimetric inequality for the first non-zero eigenvalue of a weighted Neumann problem.</description><subject>Mathematics - Optimization and Control</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotz71OwzAUhmEvDKhwAUz4BhL8EyfxCBUUpEoM7R6d2OdQS2lcHPfv7oHS6VtefdLD2IMUZdUaI54gncKhVFrKUkjR6lv2strADnkkjqeccAsDp_3ocojjxCkmfsTwtcno-Sr2ccBDkc-_fRjxew9DyAGnO3ZDMEx4f90ZW7-9rufvxfJz8TF_XhZQN7poSGnoW2krFI02va2Vldr6Rnon0DtwQpF35AxpX4EhVfXKWqpl66WRoGfs8f_2guh2KWwhnbs_THfB6B8ZT0Vd</recordid><startdate>20231102</startdate><enddate>20231102</enddate><creator>Brock, Friedemann</creator><creator>Chiacchio, Francesco</creator><creator>Croce, Gisella</creator><creator>Mercaldo, Anna</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20231102</creationdate><title>Shape of extremal functions for weighted Sobolev-type inequalities</title><author>Brock, Friedemann ; Chiacchio, Francesco ; Croce, Gisella ; Mercaldo, Anna</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a673-7f23ab8194e0735b9629139d71dc0edcac02fdcfc5f3d4a5f24b299f618d151a3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Mathematics - Optimization and Control</topic><toplevel>online_resources</toplevel><creatorcontrib>Brock, Friedemann</creatorcontrib><creatorcontrib>Chiacchio, Francesco</creatorcontrib><creatorcontrib>Croce, Gisella</creatorcontrib><creatorcontrib>Mercaldo, Anna</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Brock, Friedemann</au><au>Chiacchio, Francesco</au><au>Croce, Gisella</au><au>Mercaldo, Anna</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Shape of extremal functions for weighted Sobolev-type inequalities</atitle><date>2023-11-02</date><risdate>2023</risdate><abstract>We study the shape of solutions to some variational problems in Sobolev spaces with weights that are powers of |x|. In particular, we detect situations when the extremal functions lack symmetry properties such as radial symmetry and antisymmetry. We also prove an isoperimetric inequality for the first non-zero eigenvalue of a weighted Neumann problem.</abstract><doi>10.48550/arxiv.2311.01083</doi><oa>free_for_read</oa></addata></record>
fulltext fulltext_linktorsrc
identifier DOI: 10.48550/arxiv.2311.01083
ispartof
issn
language eng
recordid cdi_arxiv_primary_2311_01083
source arXiv.org
subjects Mathematics - Optimization and Control
title Shape of extremal functions for weighted Sobolev-type inequalities
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-25T16%3A01%3A12IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-arxiv_GOX&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Shape%20of%20extremal%20functions%20for%20weighted%20Sobolev-type%20inequalities&rft.au=Brock,%20Friedemann&rft.date=2023-11-02&rft_id=info:doi/10.48550/arxiv.2311.01083&rft_dat=%3Carxiv_GOX%3E2311_01083%3C/arxiv_GOX%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true