Loading…
Trudinger-Moser inequalities involving fast growth and weights with strong vanishing at zero
In this paper we study some weighted Trudinger-Moser type problems, namely sF,h=supu∈H,‖u‖H=1∫BF(u)h(|x|)dx,\begin{equation*} \displaystyle {s_{F,h} = \sup _{u \in H, \, \| u\|_H =1 } \int _{B} F(u) h(|x|) dx}, \end{equation*} where B⊂R2B \subset {\mathbb R}^2 represents the open unit ball centered...
Saved in:
| Published in: | Proceedings of the American Mathematical Society 2016-08, Vol.144 (8), p.3369-3380 |
|---|---|
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
| Subjects: | |
| Citations: | Items that this one cites Items that cite this one |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| cited_by | cdi_FETCH-LOGICAL-a338t-fb0edb2e8426a4a189a17c10a5297a6fd54eb2eb69cc2e20d7d9b7209826bada3 |
|---|---|
| cites | cdi_FETCH-LOGICAL-a338t-fb0edb2e8426a4a189a17c10a5297a6fd54eb2eb69cc2e20d7d9b7209826bada3 |
| container_end_page | 3380 |
| container_issue | 8 |
| container_start_page | 3369 |
| container_title | Proceedings of the American Mathematical Society |
| container_volume | 144 |
| creator | de Figueiredo, Djairo G. do Ó, João Marcos B. dos Santos, Ederson Moreira |
| description | In this paper we study some weighted Trudinger-Moser type problems, namely sF,h=supu∈H,‖u‖H=1∫BF(u)h(|x|)dx,\begin{equation*} \displaystyle {s_{F,h} = \sup _{u \in H, \, \| u\|_H =1 } \int _{B} F(u) h(|x|) dx}, \end{equation*} where B⊂R2B \subset {\mathbb R}^2 represents the open unit ball centered at zero in R2{\mathbb R}^2 and HH stands either for H0,rad1(B)H^1_{0, \textrm {rad}}(B) or Hrad1(B)H^1_{\textrm {rad}}(B). We present the precise balance between h(r)h(r) and F(t)F(t) that guarantees sF,hs_{F,h} to be finite. We prove that sF,hs_{F,h} is attained up to the h(r)h(r)-radially critical case. In particular, we solve two open problems in the critical growth case. |
| doi_str_mv | 10.1090/proc/13114 |
| format | article |
| fullrecord | <record><control><sourceid>jstor_cross</sourceid><recordid>TN_cdi_crossref_primary_10_1090_proc_13114</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><jstor_id>procamermathsoci.144.8.3369</jstor_id><sourcerecordid>procamermathsoci.144.8.3369</sourcerecordid><originalsourceid>FETCH-LOGICAL-a338t-fb0edb2e8426a4a189a17c10a5297a6fd54eb2eb69cc2e20d7d9b7209826bada3</originalsourceid><addsrcrecordid>eNp9kE9LAzEQxYMoWKsXP0EuXoS1-bPdTY5StAoVL_UmhNlNtpvS3dQkbdFPb9aKR0_Dm_d7A_MQuqbkjhJJJlvv6gnllOYnaESJEFkhWHGKRoQQlknJ5Tm6CGGdJJV5OULvS7_Ttl8Zn724YDy2vfnYwcZGa0ISe7fZJxs3ECJeeXeILYZe44OxqzYGfLBpEaJ3idlDb0M70BDxl_HuEp01sAnm6neO0dvjw3L2lC1e58-z-0UGnIuYNRUxumJG5KyAHKiQQMuaEpgyWULR6Glukl0Vsq6ZYUSXWlYlIzK9VoEGPka3x7u1dyF406ittx34T0WJGnpRQy_qp5cEkyO8DtH5P3IgoDO-g9gGV1tF81wJxXkhU-TmGIEu_Hf6GzQNdpk</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Trudinger-Moser inequalities involving fast growth and weights with strong vanishing at zero</title><source>JSTOR Archival Journals and Primary Sources Collection</source><source>American Mathematical Society Publications (Freely Accessible)</source><creator>de Figueiredo, Djairo G. ; do Ó, João Marcos B. ; dos Santos, Ederson Moreira</creator><creatorcontrib>de Figueiredo, Djairo G. ; do Ó, João Marcos B. ; dos Santos, Ederson Moreira</creatorcontrib><description>In this paper we study some weighted Trudinger-Moser type problems, namely sF,h=supu∈H,‖u‖H=1∫BF(u)h(|x|)dx,\begin{equation*} \displaystyle {s_{F,h} = \sup _{u \in H, \, \| u\|_H =1 } \int _{B} F(u) h(|x|) dx}, \end{equation*} where B⊂R2B \subset {\mathbb R}^2 represents the open unit ball centered at zero in R2{\mathbb R}^2 and HH stands either for H0,rad1(B)H^1_{0, \textrm {rad}}(B) or Hrad1(B)H^1_{\textrm {rad}}(B). We present the precise balance between h(r)h(r) and F(t)F(t) that guarantees sF,hs_{F,h} to be finite. We prove that sF,hs_{F,h} is attained up to the h(r)h(r)-radially critical case. In particular, we solve two open problems in the critical growth case.</description><identifier>ISSN: 0002-9939</identifier><identifier>EISSN: 1088-6826</identifier><identifier>DOI: 10.1090/proc/13114</identifier><language>eng</language><publisher>Providence, Rhode Island: American Mathematical Society</publisher><subject>B. ANALYSIS ; Research article</subject><ispartof>Proceedings of the American Mathematical Society, 2016-08, Vol.144 (8), p.3369-3380</ispartof><rights>Copyright 2016 American Mathematical Society</rights><rights>2016 American Mathematical Society</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-a338t-fb0edb2e8426a4a189a17c10a5297a6fd54eb2eb69cc2e20d7d9b7209826bada3</citedby><cites>FETCH-LOGICAL-a338t-fb0edb2e8426a4a189a17c10a5297a6fd54eb2eb69cc2e20d7d9b7209826bada3</cites><orcidid>0000-0002-9902-244X</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.ams.org/proc/2016-144-08/S0002-9939-2016-13114-6/S0002-9939-2016-13114-6.pdf$$EPDF$$P50$$Gams$$H</linktopdf><linktohtml>$$Uhttps://www.ams.org/proc/2016-144-08/S0002-9939-2016-13114-6/$$EHTML$$P50$$Gams$$H</linktohtml><link.rule.ids>69,314,776,780,23303,27901,27902,58213,58446,77580,77590</link.rule.ids></links><search><creatorcontrib>de Figueiredo, Djairo G.</creatorcontrib><creatorcontrib>do Ó, João Marcos B.</creatorcontrib><creatorcontrib>dos Santos, Ederson Moreira</creatorcontrib><title>Trudinger-Moser inequalities involving fast growth and weights with strong vanishing at zero</title><title>Proceedings of the American Mathematical Society</title><addtitle>Proc. Amer. Math. Soc</addtitle><description>In this paper we study some weighted Trudinger-Moser type problems, namely sF,h=supu∈H,‖u‖H=1∫BF(u)h(|x|)dx,\begin{equation*} \displaystyle {s_{F,h} = \sup _{u \in H, \, \| u\|_H =1 } \int _{B} F(u) h(|x|) dx}, \end{equation*} where B⊂R2B \subset {\mathbb R}^2 represents the open unit ball centered at zero in R2{\mathbb R}^2 and HH stands either for H0,rad1(B)H^1_{0, \textrm {rad}}(B) or Hrad1(B)H^1_{\textrm {rad}}(B). We present the precise balance between h(r)h(r) and F(t)F(t) that guarantees sF,hs_{F,h} to be finite. We prove that sF,hs_{F,h} is attained up to the h(r)h(r)-radially critical case. In particular, we solve two open problems in the critical growth case.</description><subject>B. ANALYSIS</subject><subject>Research article</subject><issn>0002-9939</issn><issn>1088-6826</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><recordid>eNp9kE9LAzEQxYMoWKsXP0EuXoS1-bPdTY5StAoVL_UmhNlNtpvS3dQkbdFPb9aKR0_Dm_d7A_MQuqbkjhJJJlvv6gnllOYnaESJEFkhWHGKRoQQlknJ5Tm6CGGdJJV5OULvS7_Ttl8Zn724YDy2vfnYwcZGa0ISe7fZJxs3ECJeeXeILYZe44OxqzYGfLBpEaJ3idlDb0M70BDxl_HuEp01sAnm6neO0dvjw3L2lC1e58-z-0UGnIuYNRUxumJG5KyAHKiQQMuaEpgyWULR6Glukl0Vsq6ZYUSXWlYlIzK9VoEGPka3x7u1dyF406ittx34T0WJGnpRQy_qp5cEkyO8DtH5P3IgoDO-g9gGV1tF81wJxXkhU-TmGIEu_Hf6GzQNdpk</recordid><startdate>20160801</startdate><enddate>20160801</enddate><creator>de Figueiredo, Djairo G.</creator><creator>do Ó, João Marcos B.</creator><creator>dos Santos, Ederson Moreira</creator><general>American Mathematical Society</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0002-9902-244X</orcidid></search><sort><creationdate>20160801</creationdate><title>Trudinger-Moser inequalities involving fast growth and weights with strong vanishing at zero</title><author>de Figueiredo, Djairo G. ; do Ó, João Marcos B. ; dos Santos, Ederson Moreira</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a338t-fb0edb2e8426a4a189a17c10a5297a6fd54eb2eb69cc2e20d7d9b7209826bada3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2016</creationdate><topic>B. ANALYSIS</topic><topic>Research article</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>de Figueiredo, Djairo G.</creatorcontrib><creatorcontrib>do Ó, João Marcos B.</creatorcontrib><creatorcontrib>dos Santos, Ederson Moreira</creatorcontrib><collection>CrossRef</collection><jtitle>Proceedings of the American Mathematical Society</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>de Figueiredo, Djairo G.</au><au>do Ó, João Marcos B.</au><au>dos Santos, Ederson Moreira</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Trudinger-Moser inequalities involving fast growth and weights with strong vanishing at zero</atitle><jtitle>Proceedings of the American Mathematical Society</jtitle><stitle>Proc. Amer. Math. Soc</stitle><date>2016-08-01</date><risdate>2016</risdate><volume>144</volume><issue>8</issue><spage>3369</spage><epage>3380</epage><pages>3369-3380</pages><issn>0002-9939</issn><eissn>1088-6826</eissn><abstract>In this paper we study some weighted Trudinger-Moser type problems, namely sF,h=supu∈H,‖u‖H=1∫BF(u)h(|x|)dx,\begin{equation*} \displaystyle {s_{F,h} = \sup _{u \in H, \, \| u\|_H =1 } \int _{B} F(u) h(|x|) dx}, \end{equation*} where B⊂R2B \subset {\mathbb R}^2 represents the open unit ball centered at zero in R2{\mathbb R}^2 and HH stands either for H0,rad1(B)H^1_{0, \textrm {rad}}(B) or Hrad1(B)H^1_{\textrm {rad}}(B). We present the precise balance between h(r)h(r) and F(t)F(t) that guarantees sF,hs_{F,h} to be finite. We prove that sF,hs_{F,h} is attained up to the h(r)h(r)-radially critical case. In particular, we solve two open problems in the critical growth case.</abstract><cop>Providence, Rhode Island</cop><pub>American Mathematical Society</pub><doi>10.1090/proc/13114</doi><tpages>12</tpages><orcidid>https://orcid.org/0000-0002-9902-244X</orcidid><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0002-9939 |
| ispartof | Proceedings of the American Mathematical Society, 2016-08, Vol.144 (8), p.3369-3380 |
| issn | 0002-9939 1088-6826 |
| language | eng |
| recordid | cdi_crossref_primary_10_1090_proc_13114 |
| source | JSTOR Archival Journals and Primary Sources Collection; American Mathematical Society Publications (Freely Accessible) |
| subjects | B. ANALYSIS Research article |
| title | Trudinger-Moser inequalities involving fast growth and weights with strong vanishing at zero |
| url | http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-08T09%3A55%3A24IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-jstor_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Trudinger-Moser%20inequalities%20involving%20fast%20growth%20and%20weights%20with%20strong%20vanishing%20at%20zero&rft.jtitle=Proceedings%20of%20the%20American%20Mathematical%20Society&rft.au=de%20Figueiredo,%20Djairo%20G.&rft.date=2016-08-01&rft.volume=144&rft.issue=8&rft.spage=3369&rft.epage=3380&rft.pages=3369-3380&rft.issn=0002-9939&rft.eissn=1088-6826&rft_id=info:doi/10.1090/proc/13114&rft_dat=%3Cjstor_cross%3Eprocamermathsoci.144.8.3369%3C/jstor_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-a338t-fb0edb2e8426a4a189a17c10a5297a6fd54eb2eb69cc2e20d7d9b7209826bada3%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_id=info:pmid/&rft_jstor_id=procamermathsoci.144.8.3369&rfr_iscdi=true |