Weighted Lorentz estimates for non-uniformly elliptic problems with variable exponents
In this paper, a global L ω s , t -bound for the gradient of weak solutions to non-uniformly nonlinear elliptic equations with variable exponents is presented. The main difficulties arise from variable ( p ( · ) , q ( · ) ) -growth conditions can be handled by standard techniques. Under the appropri...
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| Veröffentlicht in: | Manuscripta mathematica 2023-11, Vol.172 (3-4), p.1227-1244 |
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| creator | Tran, Minh-Phuong Nguyen, Thanh-Nhan Pham, Le-Tuyet-Nhi Dang, Thi-Thanh-Truc |
| description | In this paper, a global
L
ω
s
,
t
-bound for the gradient of weak solutions to non-uniformly nonlinear elliptic equations with variable exponents is presented. The main difficulties arise from variable
(
p
(
·
)
,
q
(
·
)
)
-growth conditions can be handled by standard techniques. Under the appropriated assumptions and minimal regularity on initial data of the problem, weighted regularity estimates in the frame of Lorentz spaces will be established. Furthermore, the use of level-set inequalities on distribution functions is also imposed to obtained the norm bounds in a wide range of generalized Lebesgue spaces such as Lorentz, Lorentz-Morrey or Orlicz spaces, etc. |
| doi_str_mv | 10.1007/s00229-022-01452-5 |
| format | Article |
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L
ω
s
,
t
-bound for the gradient of weak solutions to non-uniformly nonlinear elliptic equations with variable exponents is presented. The main difficulties arise from variable
(
p
(
·
)
,
q
(
·
)
)
-growth conditions can be handled by standard techniques. Under the appropriated assumptions and minimal regularity on initial data of the problem, weighted regularity estimates in the frame of Lorentz spaces will be established. Furthermore, the use of level-set inequalities on distribution functions is also imposed to obtained the norm bounds in a wide range of generalized Lebesgue spaces such as Lorentz, Lorentz-Morrey or Orlicz spaces, etc.</description><identifier>ISSN: 0025-2611</identifier><identifier>EISSN: 1432-1785</identifier><identifier>DOI: 10.1007/s00229-022-01452-5</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Algebraic Geometry ; Calculus of Variations and Optimal Control; Optimization ; Distribution functions ; Elliptic functions ; Estimates ; Exponents ; Geometry ; Lie Groups ; Mathematics ; Mathematics and Statistics ; Number Theory ; Regularity ; Topological Groups</subject><ispartof>Manuscripta mathematica, 2023-11, Vol.172 (3-4), p.1227-1244</ispartof><rights>The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-4aeeeec58f7975f34ad91b69204bdcea0478bec052f82d870afff706876aa34c3</citedby><cites>FETCH-LOGICAL-c319t-4aeeeec58f7975f34ad91b69204bdcea0478bec052f82d870afff706876aa34c3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00229-022-01452-5$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00229-022-01452-5$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Tran, Minh-Phuong</creatorcontrib><creatorcontrib>Nguyen, Thanh-Nhan</creatorcontrib><creatorcontrib>Pham, Le-Tuyet-Nhi</creatorcontrib><creatorcontrib>Dang, Thi-Thanh-Truc</creatorcontrib><title>Weighted Lorentz estimates for non-uniformly elliptic problems with variable exponents</title><title>Manuscripta mathematica</title><addtitle>manuscripta math</addtitle><description>In this paper, a global
L
ω
s
,
t
-bound for the gradient of weak solutions to non-uniformly nonlinear elliptic equations with variable exponents is presented. The main difficulties arise from variable
(
p
(
·
)
,
q
(
·
)
)
-growth conditions can be handled by standard techniques. Under the appropriated assumptions and minimal regularity on initial data of the problem, weighted regularity estimates in the frame of Lorentz spaces will be established. Furthermore, the use of level-set inequalities on distribution functions is also imposed to obtained the norm bounds in a wide range of generalized Lebesgue spaces such as Lorentz, Lorentz-Morrey or Orlicz spaces, etc.</description><subject>Algebraic Geometry</subject><subject>Calculus of Variations and Optimal Control; Optimization</subject><subject>Distribution functions</subject><subject>Elliptic functions</subject><subject>Estimates</subject><subject>Exponents</subject><subject>Geometry</subject><subject>Lie Groups</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Number Theory</subject><subject>Regularity</subject><subject>Topological Groups</subject><issn>0025-2611</issn><issn>1432-1785</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp9UMtOwzAQtBBIlMIPcLLE2eBn7BwR4iVV4sLjaDmO3aZKk2CnQPl6FoLEjT3MruWZ8XoQOmX0nFGqLzKlnJcEgFAmFSdqD82YFJwwbdQ-msG9Irxg7BAd5bymwBJazNDzS2iWqzHUeNGn0I2fOOSx2bgxZBz7hLu-I9uugXHT7nBo22YYG4-H1Fdt2GT83owr_OZS4-CMw8fQd-CSj9FBdG0OJ799jp5urh-v7sji4fb-6nJBvGDlSKQLUF6ZqEutopCuLllVlJzKqvbBUalNFTxVPBpeG01djFHTwujCOSG9mKOzyRcWet3C6nbdb1MHT1putNBGSqaBxSeWT33OKUQ7JPhj2llG7Xd-dsrPAtif_KwCkZhEGcjdMqQ_639UX_aedO8</recordid><startdate>20231101</startdate><enddate>20231101</enddate><creator>Tran, Minh-Phuong</creator><creator>Nguyen, Thanh-Nhan</creator><creator>Pham, Le-Tuyet-Nhi</creator><creator>Dang, Thi-Thanh-Truc</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20231101</creationdate><title>Weighted Lorentz estimates for non-uniformly elliptic problems with variable exponents</title><author>Tran, Minh-Phuong ; Nguyen, Thanh-Nhan ; Pham, Le-Tuyet-Nhi ; Dang, Thi-Thanh-Truc</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-4aeeeec58f7975f34ad91b69204bdcea0478bec052f82d870afff706876aa34c3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Algebraic Geometry</topic><topic>Calculus of Variations and Optimal Control; Optimization</topic><topic>Distribution functions</topic><topic>Elliptic functions</topic><topic>Estimates</topic><topic>Exponents</topic><topic>Geometry</topic><topic>Lie Groups</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Number Theory</topic><topic>Regularity</topic><topic>Topological Groups</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Tran, Minh-Phuong</creatorcontrib><creatorcontrib>Nguyen, Thanh-Nhan</creatorcontrib><creatorcontrib>Pham, Le-Tuyet-Nhi</creatorcontrib><creatorcontrib>Dang, Thi-Thanh-Truc</creatorcontrib><collection>CrossRef</collection><jtitle>Manuscripta mathematica</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Tran, Minh-Phuong</au><au>Nguyen, Thanh-Nhan</au><au>Pham, Le-Tuyet-Nhi</au><au>Dang, Thi-Thanh-Truc</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Weighted Lorentz estimates for non-uniformly elliptic problems with variable exponents</atitle><jtitle>Manuscripta mathematica</jtitle><stitle>manuscripta math</stitle><date>2023-11-01</date><risdate>2023</risdate><volume>172</volume><issue>3-4</issue><spage>1227</spage><epage>1244</epage><pages>1227-1244</pages><issn>0025-2611</issn><eissn>1432-1785</eissn><abstract>In this paper, a global
L
ω
s
,
t
-bound for the gradient of weak solutions to non-uniformly nonlinear elliptic equations with variable exponents is presented. The main difficulties arise from variable
(
p
(
·
)
,
q
(
·
)
)
-growth conditions can be handled by standard techniques. Under the appropriated assumptions and minimal regularity on initial data of the problem, weighted regularity estimates in the frame of Lorentz spaces will be established. Furthermore, the use of level-set inequalities on distribution functions is also imposed to obtained the norm bounds in a wide range of generalized Lebesgue spaces such as Lorentz, Lorentz-Morrey or Orlicz spaces, etc.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s00229-022-01452-5</doi><tpages>18</tpages></addata></record> |
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| source | Springer Nature - Complete Springer Journals |
| subjects | Algebraic Geometry Calculus of Variations and Optimal Control Optimization Distribution functions Elliptic functions Estimates Exponents Geometry Lie Groups Mathematics Mathematics and Statistics Number Theory Regularity Topological Groups |
| title | Weighted Lorentz estimates for non-uniformly elliptic problems with variable exponents |
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