Qualitative properties for elliptic problems with CKN operators

The purpose of this paper is to study basic property of the operator $$\mathcal{L}_{\mu_1,\mu_2} u=-\Delta +\frac{\mu_1 }{|x|^2}x\cdot\nabla +\frac{\mu_2 }{|x|^2},$$ which generates at the origin due to the critical gradient and the Hardy term, where \(\mu_1,\mu_2\) are free parameters. This operato...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2022-06
Main Authors: Chen, Huyuan, Zheng, Yishan
Format: Article
Language:English
Subjects:
Liouville theorem
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by
cites
container_end_page
container_issue
container_start_page
container_title arXiv.org
container_volume
creator Chen, Huyuan
Zheng, Yishan
description The purpose of this paper is to study basic property of the operator $$\mathcal{L}_{\mu_1,\mu_2} u=-\Delta +\frac{\mu_1 }{|x|^2}x\cdot\nabla +\frac{\mu_2 }{|x|^2},$$ which generates at the origin due to the critical gradient and the Hardy term, where \(\mu_1,\mu_2\) are free parameters. This operator arises from the critical Caffarelli-Kohn-Nirenberg inequality. We analyze the fundamental solutions in a weighted distributional identity and obtain the Liouville theorem for the Lane-Emden equation with that operator, by using the classification of isolated singular solutions of the related Poisson problem in a bounded domain \(\Omega \subset \mathbb{R}^N\) (\(N \geq 2\)) containing the origin.
format article
fullrecord <record><control><sourceid>proquest</sourceid><recordid>TN_cdi_proquest_journals_2675089513</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2675089513</sourcerecordid><originalsourceid>FETCH-proquest_journals_26750895133</originalsourceid><addsrcrecordid>eNpjYuA0MjY21LUwMTLiYOAtLs4yMDAwMjM3MjU15mSwDyxNzMksSSzJLEtVKCjKL0gtKslMLVZIyy9SSM3JySwoyUwGiSflpOYWK5RnlmQoOHv7KYDUJZbkFxXzMLCmJeYUp_JCaW4GZTfXEGcPXaCewtLU4pL4rPzSojygVDzQTlMDC0tTQ2Nj4lQBAE8pOU4</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2675089513</pqid></control><display><type>article</type><title>Qualitative properties for elliptic problems with CKN operators</title><source>Publicly Available Content Database</source><creator>Chen, Huyuan ; Zheng, Yishan</creator><creatorcontrib>Chen, Huyuan ; Zheng, Yishan</creatorcontrib><description>The purpose of this paper is to study basic property of the operator $$\mathcal{L}_{\mu_1,\mu_2} u=-\Delta +\frac{\mu_1 }{|x|^2}x\cdot\nabla +\frac{\mu_2 }{|x|^2},$$ which generates at the origin due to the critical gradient and the Hardy term, where \(\mu_1,\mu_2\) are free parameters. This operator arises from the critical Caffarelli-Kohn-Nirenberg inequality. We analyze the fundamental solutions in a weighted distributional identity and obtain the Liouville theorem for the Lane-Emden equation with that operator, by using the classification of isolated singular solutions of the related Poisson problem in a bounded domain \(\Omega \subset \mathbb{R}^N\) (\(N \geq 2\)) containing the origin.</description><identifier>EISSN: 2331-8422</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Liouville theorem</subject><ispartof>arXiv.org, 2022-06</ispartof><rights>2022. This work is published under http://creativecommons.org/licenses/by-sa/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.proquest.com/docview/2675089513?pq-origsite=primo$$EHTML$$P50$$Gproquest$$Hfree_for_read</linktohtml><link.rule.ids>780,784,25752,37011,44589</link.rule.ids></links><search><creatorcontrib>Chen, Huyuan</creatorcontrib><creatorcontrib>Zheng, Yishan</creatorcontrib><title>Qualitative properties for elliptic problems with CKN operators</title><title>arXiv.org</title><description>The purpose of this paper is to study basic property of the operator $$\mathcal{L}_{\mu_1,\mu_2} u=-\Delta +\frac{\mu_1 }{|x|^2}x\cdot\nabla +\frac{\mu_2 }{|x|^2},$$ which generates at the origin due to the critical gradient and the Hardy term, where \(\mu_1,\mu_2\) are free parameters. This operator arises from the critical Caffarelli-Kohn-Nirenberg inequality. We analyze the fundamental solutions in a weighted distributional identity and obtain the Liouville theorem for the Lane-Emden equation with that operator, by using the classification of isolated singular solutions of the related Poisson problem in a bounded domain \(\Omega \subset \mathbb{R}^N\) (\(N \geq 2\)) containing the origin.</description><subject>Liouville theorem</subject><issn>2331-8422</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><sourceid>PIMPY</sourceid><recordid>eNpjYuA0MjY21LUwMTLiYOAtLs4yMDAwMjM3MjU15mSwDyxNzMksSSzJLEtVKCjKL0gtKslMLVZIyy9SSM3JySwoyUwGiSflpOYWK5RnlmQoOHv7KYDUJZbkFxXzMLCmJeYUp_JCaW4GZTfXEGcPXaCewtLU4pL4rPzSojygVDzQTlMDC0tTQ2Nj4lQBAE8pOU4</recordid><startdate>20220609</startdate><enddate>20220609</enddate><creator>Chen, Huyuan</creator><creator>Zheng, Yishan</creator><general>Cornell University Library, arXiv.org</general><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>L6V</scope><scope>M7S</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope></search><sort><creationdate>20220609</creationdate><title>Qualitative properties for elliptic problems with CKN operators</title><author>Chen, Huyuan ; Zheng, Yishan</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-proquest_journals_26750895133</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Liouville theorem</topic><toplevel>online_resources</toplevel><creatorcontrib>Chen, Huyuan</creatorcontrib><creatorcontrib>Zheng, Yishan</creatorcontrib><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science &amp; Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Publicly Available Content Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Chen, Huyuan</au><au>Zheng, Yishan</au><format>book</format><genre>document</genre><ristype>GEN</ristype><atitle>Qualitative properties for elliptic problems with CKN operators</atitle><jtitle>arXiv.org</jtitle><date>2022-06-09</date><risdate>2022</risdate><eissn>2331-8422</eissn><abstract>The purpose of this paper is to study basic property of the operator $$\mathcal{L}_{\mu_1,\mu_2} u=-\Delta +\frac{\mu_1 }{|x|^2}x\cdot\nabla +\frac{\mu_2 }{|x|^2},$$ which generates at the origin due to the critical gradient and the Hardy term, where \(\mu_1,\mu_2\) are free parameters. This operator arises from the critical Caffarelli-Kohn-Nirenberg inequality. We analyze the fundamental solutions in a weighted distributional identity and obtain the Liouville theorem for the Lane-Emden equation with that operator, by using the classification of isolated singular solutions of the related Poisson problem in a bounded domain \(\Omega \subset \mathbb{R}^N\) (\(N \geq 2\)) containing the origin.</abstract><cop>Ithaca</cop><pub>Cornell University Library, arXiv.org</pub><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier EISSN: 2331-8422
ispartof arXiv.org, 2022-06
issn 2331-8422
language eng
recordid cdi_proquest_journals_2675089513
source Publicly Available Content Database
subjects Liouville theorem
title Qualitative properties for elliptic problems with CKN operators
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-10T09%3A33%3A55IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest&rft_val_fmt=info:ofi/fmt:kev:mtx:book&rft.genre=document&rft.atitle=Qualitative%20properties%20for%20elliptic%20problems%20with%20CKN%20operators&rft.jtitle=arXiv.org&rft.au=Chen,%20Huyuan&rft.date=2022-06-09&rft.eissn=2331-8422&rft_id=info:doi/&rft_dat=%3Cproquest%3E2675089513%3C/proquest%3E%3Cgrp_id%3Ecdi_FETCH-proquest_journals_26750895133%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=2675089513&rft_id=info:pmid/&rfr_iscdi=true