Positive Liouville theorem and asymptotic behaviour for \((p,A)\)-Laplacian type elliptic equations with Fuchsian potentials in Morrey space
We study Liouville-type theorems and the asymptotic behaviour of positive solutions near an isolated singular point \(\zeta\in\partial\Omega\cup\{\infty\}\) of the quasilinear elliptic equations $$-\text{div}(|\nabla u|_A^{p-2}A\nabla u)+V|u|^{p-2}u =0\quad\text{in } \Omega\setminus\{\zeta\},$$ wher...
Gespeichert in:
| Veröffentlicht in: | arXiv.org 2020-07 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | |
|---|---|
| container_issue | |
| container_start_page | |
| container_title | arXiv.org |
| container_volume | |
| creator | Ratan Kr Giri Pinchover, Yehuda |
| description | We study Liouville-type theorems and the asymptotic behaviour of positive solutions near an isolated singular point \(\zeta\in\partial\Omega\cup\{\infty\}\) of the quasilinear elliptic equations $$-\text{div}(|\nabla u|_A^{p-2}A\nabla u)+V|u|^{p-2}u =0\quad\text{in } \Omega\setminus\{\zeta\},$$ where \(\Omega\) is a domain in \(\mathbb{R}^d\) (\(d\geq 2\)), and \(A=(a_{ij})\in L_{\rm loc}^{\infty}(\Omega;\mathbb{R}^{d\times d})\) is a symmetric and locally uniformly positive definite matrix. The potential \(V\) lies in a certain local Morrey space (depending on \(p\)) and has a Fuchsian-type isolated singularity at \(\zeta\). |
| format | Article |
| fullrecord | <record><control><sourceid>proquest</sourceid><recordid>TN_cdi_proquest_journals_2420905917</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2420905917</sourcerecordid><originalsourceid>FETCH-proquest_journals_24209059173</originalsourceid><addsrcrecordid>eNqNzUFKA0EQBdBGEBI0dyhwk4ADnZ6MMUsRg4sIWbgMhHJSYSp0ujtdNSNzBw_tBDyAqw__P_g3ZuzKcl48L5wbmYnIyVrrnpauqsqx-dlGYeWOYMOx7dh7Am0oZjoDhgOg9OekUbmGL2qwG1CGY8ywm07T48tsNys2mDzWjAG0TwTkPaerp0uLyjEIfLM2sG7rRq4qRaWgjF6AA3zEnKkHSVjTvbk9DjVN_vLOPKzfPl_fi5TjpSXR_Wm4D8O0dwtnV7ZazZfl_9QvdflVUg</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2420905917</pqid></control><display><type>article</type><title>Positive Liouville theorem and asymptotic behaviour for \((p,A)\)-Laplacian type elliptic equations with Fuchsian potentials in Morrey space</title><source>Free E- Journals</source><creator>Ratan Kr Giri ; Pinchover, Yehuda</creator><creatorcontrib>Ratan Kr Giri ; Pinchover, Yehuda</creatorcontrib><description>We study Liouville-type theorems and the asymptotic behaviour of positive solutions near an isolated singular point \(\zeta\in\partial\Omega\cup\{\infty\}\) of the quasilinear elliptic equations $$-\text{div}(|\nabla u|_A^{p-2}A\nabla u)+V|u|^{p-2}u =0\quad\text{in } \Omega\setminus\{\zeta\},$$ where \(\Omega\) is a domain in \(\mathbb{R}^d\) (\(d\geq 2\)), and \(A=(a_{ij})\in L_{\rm loc}^{\infty}(\Omega;\mathbb{R}^{d\times d})\) is a symmetric and locally uniformly positive definite matrix. The potential \(V\) lies in a certain local Morrey space (depending on \(p\)) and has a Fuchsian-type isolated singularity at \(\zeta\).</description><identifier>EISSN: 2331-8422</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Asymptotic properties ; Elliptic functions ; Liouville theorem ; Mathematical analysis ; Matrix methods ; Singularity (mathematics)</subject><ispartof>arXiv.org, 2020-07</ispartof><rights>2020. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (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><link.rule.ids>780,784</link.rule.ids></links><search><creatorcontrib>Ratan Kr Giri</creatorcontrib><creatorcontrib>Pinchover, Yehuda</creatorcontrib><title>Positive Liouville theorem and asymptotic behaviour for \((p,A)\)-Laplacian type elliptic equations with Fuchsian potentials in Morrey space</title><title>arXiv.org</title><description>We study Liouville-type theorems and the asymptotic behaviour of positive solutions near an isolated singular point \(\zeta\in\partial\Omega\cup\{\infty\}\) of the quasilinear elliptic equations $$-\text{div}(|\nabla u|_A^{p-2}A\nabla u)+V|u|^{p-2}u =0\quad\text{in } \Omega\setminus\{\zeta\},$$ where \(\Omega\) is a domain in \(\mathbb{R}^d\) (\(d\geq 2\)), and \(A=(a_{ij})\in L_{\rm loc}^{\infty}(\Omega;\mathbb{R}^{d\times d})\) is a symmetric and locally uniformly positive definite matrix. The potential \(V\) lies in a certain local Morrey space (depending on \(p\)) and has a Fuchsian-type isolated singularity at \(\zeta\).</description><subject>Asymptotic properties</subject><subject>Elliptic functions</subject><subject>Liouville theorem</subject><subject>Mathematical analysis</subject><subject>Matrix methods</subject><subject>Singularity (mathematics)</subject><issn>2331-8422</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><recordid>eNqNzUFKA0EQBdBGEBI0dyhwk4ADnZ6MMUsRg4sIWbgMhHJSYSp0ujtdNSNzBw_tBDyAqw__P_g3ZuzKcl48L5wbmYnIyVrrnpauqsqx-dlGYeWOYMOx7dh7Am0oZjoDhgOg9OekUbmGL2qwG1CGY8ywm07T48tsNys2mDzWjAG0TwTkPaerp0uLyjEIfLM2sG7rRq4qRaWgjF6AA3zEnKkHSVjTvbk9DjVN_vLOPKzfPl_fi5TjpSXR_Wm4D8O0dwtnV7ZazZfl_9QvdflVUg</recordid><startdate>20200705</startdate><enddate>20200705</enddate><creator>Ratan Kr Giri</creator><creator>Pinchover, Yehuda</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>20200705</creationdate><title>Positive Liouville theorem and asymptotic behaviour for \((p,A)\)-Laplacian type elliptic equations with Fuchsian potentials in Morrey space</title><author>Ratan Kr Giri ; Pinchover, Yehuda</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-proquest_journals_24209059173</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Asymptotic properties</topic><topic>Elliptic functions</topic><topic>Liouville theorem</topic><topic>Mathematical analysis</topic><topic>Matrix methods</topic><topic>Singularity (mathematics)</topic><toplevel>online_resources</toplevel><creatorcontrib>Ratan Kr Giri</creatorcontrib><creatorcontrib>Pinchover, Yehuda</creatorcontrib><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science & 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>Ratan Kr Giri</au><au>Pinchover, Yehuda</au><format>book</format><genre>document</genre><ristype>GEN</ristype><atitle>Positive Liouville theorem and asymptotic behaviour for \((p,A)\)-Laplacian type elliptic equations with Fuchsian potentials in Morrey space</atitle><jtitle>arXiv.org</jtitle><date>2020-07-05</date><risdate>2020</risdate><eissn>2331-8422</eissn><abstract>We study Liouville-type theorems and the asymptotic behaviour of positive solutions near an isolated singular point \(\zeta\in\partial\Omega\cup\{\infty\}\) of the quasilinear elliptic equations $$-\text{div}(|\nabla u|_A^{p-2}A\nabla u)+V|u|^{p-2}u =0\quad\text{in } \Omega\setminus\{\zeta\},$$ where \(\Omega\) is a domain in \(\mathbb{R}^d\) (\(d\geq 2\)), and \(A=(a_{ij})\in L_{\rm loc}^{\infty}(\Omega;\mathbb{R}^{d\times d})\) is a symmetric and locally uniformly positive definite matrix. The potential \(V\) lies in a certain local Morrey space (depending on \(p\)) and has a Fuchsian-type isolated singularity at \(\zeta\).</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, 2020-07 |
| issn | 2331-8422 |
| language | eng |
| recordid | cdi_proquest_journals_2420905917 |
| source | Free E- Journals |
| subjects | Asymptotic properties Elliptic functions Liouville theorem Mathematical analysis Matrix methods Singularity (mathematics) |
| title | Positive Liouville theorem and asymptotic behaviour for \((p,A)\)-Laplacian type elliptic equations with Fuchsian potentials in Morrey space |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-02T23%3A19%3A30IST&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=Positive%20Liouville%20theorem%20and%20asymptotic%20behaviour%20for%20%5C((p,A)%5C)-Laplacian%20type%20elliptic%20equations%20with%20Fuchsian%20potentials%20in%20Morrey%20space&rft.jtitle=arXiv.org&rft.au=Ratan%20Kr%20Giri&rft.date=2020-07-05&rft.eissn=2331-8422&rft_id=info:doi/&rft_dat=%3Cproquest%3E2420905917%3C/proquest%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2420905917&rft_id=info:pmid/&rfr_iscdi=true |