ON STRONGLY QUASILINEAR DEGENERATE ELLIPTIC SYSTEMS WITH WEAK MONOTONICITY AND NONLINEAR PHYSICAL DATA
This work is devoted to studying the quasilinear elliptic system - d i v a ( x , u , D u ) + | u | p - 2 u + b ( x , u , D u ) = v ( x ) + f ( x , u ) + d i v g ( x , u ) on a bounded open domain of R n with homogeneous Dirichlet boundary conditions. We show that there is a weak solution to this sys...
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Veröffentlicht in: | Journal of mathematical sciences (New York, N.Y.) N.Y.), 2022-09, Vol.266 (4), p.576-592 |
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container_title | Journal of mathematical sciences (New York, N.Y.) |
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creator | Hammar, Hasnae El Allalou, Chakir Melliani, Said |
description | This work is devoted to studying the quasilinear elliptic system
-
d
i
v
a
(
x
,
u
,
D
u
)
+
|
u
|
p
-
2
u
+
b
(
x
,
u
,
D
u
)
=
v
(
x
)
+
f
(
x
,
u
)
+
d
i
v
g
(
x
,
u
)
on a bounded open domain of
R
n
with homogeneous Dirichlet boundary conditions. We show that there is a weak solution to this system under regularity, growth, and coercivity conditions for
a
, but only with very moderate monotonicity assumptions. We prove the existence result by using Galerkin’s approximation and the theory of Young measures. |
doi_str_mv | 10.1007/s10958-022-05951-4 |
format | Article |
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(
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f
(
x
,
u
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+
d
i
v
g
(
x
,
u
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on a bounded open domain of
R
n
with homogeneous Dirichlet boundary conditions. We show that there is a weak solution to this system under regularity, growth, and coercivity conditions for
a
, but only with very moderate monotonicity assumptions. We prove the existence result by using Galerkin’s approximation and the theory of Young measures.</description><identifier>ISSN: 1072-3374</identifier><identifier>EISSN: 1573-8795</identifier><identifier>DOI: 10.1007/s10958-022-05951-4</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Boundary conditions ; Coercivity ; Dirichlet problem ; Mathematics ; Mathematics and Statistics ; Original Paper</subject><ispartof>Journal of mathematical sciences (New York, N.Y.), 2022-09, Vol.266 (4), p.576-592</ispartof><rights>The Author(s), under exclusive licence to Springer Nature Switzerland AG 2022. Springer Nature or its licensor 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><rights>COPYRIGHT 2022 Springer</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c4174-3588d347af9d30c63846732ca4051e235fae9e1308a6b4ee78ef429d7643c0713</citedby><cites>FETCH-LOGICAL-c4174-3588d347af9d30c63846732ca4051e235fae9e1308a6b4ee78ef429d7643c0713</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/s10958-022-05951-4$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10958-022-05951-4$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Hammar, Hasnae El</creatorcontrib><creatorcontrib>Allalou, Chakir</creatorcontrib><creatorcontrib>Melliani, Said</creatorcontrib><title>ON STRONGLY QUASILINEAR DEGENERATE ELLIPTIC SYSTEMS WITH WEAK MONOTONICITY AND NONLINEAR PHYSICAL DATA</title><title>Journal of mathematical sciences (New York, N.Y.)</title><addtitle>J Math Sci</addtitle><description>This work is devoted to studying the quasilinear elliptic system
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v
(
x
)
+
f
(
x
,
u
)
+
d
i
v
g
(
x
,
u
)
on a bounded open domain of
R
n
with homogeneous Dirichlet boundary conditions. We show that there is a weak solution to this system under regularity, growth, and coercivity conditions for
a
, but only with very moderate monotonicity assumptions. We prove the existence result by using Galerkin’s approximation and the theory of Young measures.</description><subject>Boundary conditions</subject><subject>Coercivity</subject><subject>Dirichlet problem</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Original Paper</subject><issn>1072-3374</issn><issn>1573-8795</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><recordid>eNp9kk9r2zAYh81YYV3XL7CTYKcd1ErWXx9N4iWirtzGLiUnoTlycEnsVkpg-_ZTl0IJhKKDhHie3wsvvyT5jtEVRkhcB4wyJiFKU4hYxjCkn5JzzASBUmTsc3wjkUJCBP2SfA3hCUWJS3KedJUGdbOo9KxcgvuHvFal0kW-ANNiVuhikTcFKMpS3TVqAupl3RS3NXhUzRw8FvkNuK101VRaTVSzBLmeAl3pt4C7-bJWk7wE07zJvyVnnd0Ed_l2XyQPv4pmModlNXuFYEuxoJAwKVeECttlK4JaTiTlgqStpYhhlxLWWZc5TJC0_Dd1TkjX0TRbCU5JiwQmF8mPQ-6zH1_2LuzM07j3QxxpUiE44oJj8k6t7caZfujGnbfttg-tyQURSKacyUjBE9TaDc7bzTi4ro_fR_zVCT6eldv27Unh55EQmZ37s1vbfQhG1YtjNj2wrR9D8K4zz77fWv_XYGReK2AOFTCxAuZ_BQyNEjlIIcLD2vn3bXxg_QO3facI</recordid><startdate>20220901</startdate><enddate>20220901</enddate><creator>Hammar, Hasnae El</creator><creator>Allalou, Chakir</creator><creator>Melliani, Said</creator><general>Springer International Publishing</general><general>Springer</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>ISR</scope></search><sort><creationdate>20220901</creationdate><title>ON STRONGLY QUASILINEAR DEGENERATE ELLIPTIC SYSTEMS WITH WEAK MONOTONICITY AND NONLINEAR PHYSICAL DATA</title><author>Hammar, Hasnae El ; Allalou, Chakir ; Melliani, Said</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c4174-3588d347af9d30c63846732ca4051e235fae9e1308a6b4ee78ef429d7643c0713</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Boundary conditions</topic><topic>Coercivity</topic><topic>Dirichlet problem</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Original Paper</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Hammar, Hasnae El</creatorcontrib><creatorcontrib>Allalou, Chakir</creatorcontrib><creatorcontrib>Melliani, Said</creatorcontrib><collection>CrossRef</collection><collection>Gale In Context: Science</collection><jtitle>Journal of mathematical sciences (New York, N.Y.)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Hammar, Hasnae El</au><au>Allalou, Chakir</au><au>Melliani, Said</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>ON STRONGLY QUASILINEAR DEGENERATE ELLIPTIC SYSTEMS WITH WEAK MONOTONICITY AND NONLINEAR PHYSICAL DATA</atitle><jtitle>Journal of mathematical sciences (New York, N.Y.)</jtitle><stitle>J Math Sci</stitle><date>2022-09-01</date><risdate>2022</risdate><volume>266</volume><issue>4</issue><spage>576</spage><epage>592</epage><pages>576-592</pages><issn>1072-3374</issn><eissn>1573-8795</eissn><abstract>This work is devoted to studying the quasilinear elliptic system
-
d
i
v
a
(
x
,
u
,
D
u
)
+
|
u
|
p
-
2
u
+
b
(
x
,
u
,
D
u
)
=
v
(
x
)
+
f
(
x
,
u
)
+
d
i
v
g
(
x
,
u
)
on a bounded open domain of
R
n
with homogeneous Dirichlet boundary conditions. We show that there is a weak solution to this system under regularity, growth, and coercivity conditions for
a
, but only with very moderate monotonicity assumptions. We prove the existence result by using Galerkin’s approximation and the theory of Young measures.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s10958-022-05951-4</doi><tpages>17</tpages><oa>free_for_read</oa></addata></record> |
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issn | 1072-3374 1573-8795 |
language | eng |
recordid | cdi_proquest_journals_2776067613 |
source | Springer Nature - Complete Springer Journals |
subjects | Boundary conditions Coercivity Dirichlet problem Mathematics Mathematics and Statistics Original Paper |
title | ON STRONGLY QUASILINEAR DEGENERATE ELLIPTIC SYSTEMS WITH WEAK MONOTONICITY AND NONLINEAR PHYSICAL DATA |
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