Lower order terms in divergence form versus lower order terms with natural growth in some Dirichlet problems
We study the existence of solutions for some nonlinear elliptic boundary value problems, whose general form is: - div ( M ( x ) ∇ u ) + g ( u ) | ∇ u | 2 = - div ( E ( x , u ) ) + f ( x ) in Ω , u = 0 on ∂ Ω , where Ω is an open bounded subset of R N and f ∈ L 1 ( Ω ) . Despite this poor summability...
Gespeichert in:
| Veröffentlicht in: | Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas Físicas y Naturales. Serie A, Matemáticas, 2022-07, Vol.116 (3), Article 95 |
|---|---|
| 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 | 3 |
| container_start_page | |
| container_title | Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas |
| container_volume | 116 |
| creator | Boccardo, Lucio Polito, Andrea |
| description | We study the existence of solutions for some nonlinear elliptic boundary value problems, whose general form is:
-
div
(
M
(
x
)
∇
u
)
+
g
(
u
)
|
∇
u
|
2
=
-
div
(
E
(
x
,
u
)
)
+
f
(
x
)
in
Ω
,
u
=
0
on
∂
Ω
,
where
Ω
is an open bounded subset of
R
N
and
f
∈
L
1
(
Ω
)
. Despite this poor summability, we prove the existence of finite energy solutions due to the effect of the presence of the term
g
(
u
)
|
∇
u
|
2
. |
| doi_str_mv | 10.1007/s13398-022-01232-6 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2648760685</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2648760685</sourcerecordid><originalsourceid>FETCH-LOGICAL-c249t-ebc719b1e506b505d0ad942a021701f50015ef6cfac4c916ee173b7582fad9de3</originalsourceid><addsrcrecordid>eNp9kE1LxDAQhoMouKz7BzwFPEcnSZO0R1k_YcGLnkObTne7tM2adF3898at4EFwDvMBzzvDvIRccrjmAOYmcimLnIEQDLiQgukTMuPKFIwrUKfHPmdGgjwnixi3kELyLAczI93KHzBQH-qURwx9pO1A6_YDwxoHh7TxoadpivtIuz_soR03dCjHfSg7ug7-kMakj75HeteG1m06HOku-KrDPl6Qs6bsIi5-6py8Pdy_Lp_Y6uXxeXm7Yk5kxciwcoYXFUcFukof1FDWRSZKENwAbxQAV9ho15QucwXXiNzIyqhcNAmsUc7J1bQ3HX7fYxzt1u_DkE5aobPcaNC5SpSYKBd8jAEbuwttX4ZPy8F-G2snY20y1h6NtTqJ5CSKCR7WGH5X_6P6AkAffNY</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2648760685</pqid></control><display><type>article</type><title>Lower order terms in divergence form versus lower order terms with natural growth in some Dirichlet problems</title><source>SpringerLink Journals</source><creator>Boccardo, Lucio ; Polito, Andrea</creator><creatorcontrib>Boccardo, Lucio ; Polito, Andrea</creatorcontrib><description>We study the existence of solutions for some nonlinear elliptic boundary value problems, whose general form is:
-
div
(
M
(
x
)
∇
u
)
+
g
(
u
)
|
∇
u
|
2
=
-
div
(
E
(
x
,
u
)
)
+
f
(
x
)
in
Ω
,
u
=
0
on
∂
Ω
,
where
Ω
is an open bounded subset of
R
N
and
f
∈
L
1
(
Ω
)
. Despite this poor summability, we prove the existence of finite energy solutions due to the effect of the presence of the term
g
(
u
)
|
∇
u
|
2
.</description><identifier>ISSN: 1578-7303</identifier><identifier>EISSN: 1579-1505</identifier><identifier>DOI: 10.1007/s13398-022-01232-6</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Applications of Mathematics ; Boundary value problems ; dedicated to Professor Ildefonso Díaz on the occasion of his 70th birthday ; Dirichlet problem ; Mathematical and Computational Physics ; Mathematics ; Mathematics and Statistics ; Original Paper ; Qualitative Properties of Nonlinear Partial Differential Equations ; Theoretical</subject><ispartof>Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas, 2022-07, Vol.116 (3), Article 95</ispartof><rights>The Author(s) under exclusive licence to The Royal Academy of Sciences, Madrid 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-c249t-ebc719b1e506b505d0ad942a021701f50015ef6cfac4c916ee173b7582fad9de3</citedby><cites>FETCH-LOGICAL-c249t-ebc719b1e506b505d0ad942a021701f50015ef6cfac4c916ee173b7582fad9de3</cites><orcidid>0000-0002-8067-0121</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s13398-022-01232-6$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s13398-022-01232-6$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Boccardo, Lucio</creatorcontrib><creatorcontrib>Polito, Andrea</creatorcontrib><title>Lower order terms in divergence form versus lower order terms with natural growth in some Dirichlet problems</title><title>Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas</title><addtitle>Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat</addtitle><description>We study the existence of solutions for some nonlinear elliptic boundary value problems, whose general form is:
-
div
(
M
(
x
)
∇
u
)
+
g
(
u
)
|
∇
u
|
2
=
-
div
(
E
(
x
,
u
)
)
+
f
(
x
)
in
Ω
,
u
=
0
on
∂
Ω
,
where
Ω
is an open bounded subset of
R
N
and
f
∈
L
1
(
Ω
)
. Despite this poor summability, we prove the existence of finite energy solutions due to the effect of the presence of the term
g
(
u
)
|
∇
u
|
2
.</description><subject>Applications of Mathematics</subject><subject>Boundary value problems</subject><subject>dedicated to Professor Ildefonso Díaz on the occasion of his 70th birthday</subject><subject>Dirichlet problem</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Original Paper</subject><subject>Qualitative Properties of Nonlinear Partial Differential Equations</subject><subject>Theoretical</subject><issn>1578-7303</issn><issn>1579-1505</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><recordid>eNp9kE1LxDAQhoMouKz7BzwFPEcnSZO0R1k_YcGLnkObTne7tM2adF3898at4EFwDvMBzzvDvIRccrjmAOYmcimLnIEQDLiQgukTMuPKFIwrUKfHPmdGgjwnixi3kELyLAczI93KHzBQH-qURwx9pO1A6_YDwxoHh7TxoadpivtIuz_soR03dCjHfSg7ug7-kMakj75HeteG1m06HOku-KrDPl6Qs6bsIi5-6py8Pdy_Lp_Y6uXxeXm7Yk5kxciwcoYXFUcFukof1FDWRSZKENwAbxQAV9ho15QucwXXiNzIyqhcNAmsUc7J1bQ3HX7fYxzt1u_DkE5aobPcaNC5SpSYKBd8jAEbuwttX4ZPy8F-G2snY20y1h6NtTqJ5CSKCR7WGH5X_6P6AkAffNY</recordid><startdate>20220701</startdate><enddate>20220701</enddate><creator>Boccardo, Lucio</creator><creator>Polito, Andrea</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><orcidid>https://orcid.org/0000-0002-8067-0121</orcidid></search><sort><creationdate>20220701</creationdate><title>Lower order terms in divergence form versus lower order terms with natural growth in some Dirichlet problems</title><author>Boccardo, Lucio ; Polito, Andrea</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c249t-ebc719b1e506b505d0ad942a021701f50015ef6cfac4c916ee173b7582fad9de3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Applications of Mathematics</topic><topic>Boundary value problems</topic><topic>dedicated to Professor Ildefonso Díaz on the occasion of his 70th birthday</topic><topic>Dirichlet problem</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Original Paper</topic><topic>Qualitative Properties of Nonlinear Partial Differential Equations</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Boccardo, Lucio</creatorcontrib><creatorcontrib>Polito, Andrea</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Boccardo, Lucio</au><au>Polito, Andrea</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Lower order terms in divergence form versus lower order terms with natural growth in some Dirichlet problems</atitle><jtitle>Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas</jtitle><stitle>Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat</stitle><date>2022-07-01</date><risdate>2022</risdate><volume>116</volume><issue>3</issue><artnum>95</artnum><issn>1578-7303</issn><eissn>1579-1505</eissn><abstract>We study the existence of solutions for some nonlinear elliptic boundary value problems, whose general form is:
-
div
(
M
(
x
)
∇
u
)
+
g
(
u
)
|
∇
u
|
2
=
-
div
(
E
(
x
,
u
)
)
+
f
(
x
)
in
Ω
,
u
=
0
on
∂
Ω
,
where
Ω
is an open bounded subset of
R
N
and
f
∈
L
1
(
Ω
)
. Despite this poor summability, we prove the existence of finite energy solutions due to the effect of the presence of the term
g
(
u
)
|
∇
u
|
2
.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s13398-022-01232-6</doi><orcidid>https://orcid.org/0000-0002-8067-0121</orcidid></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1578-7303 |
| ispartof | Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas, 2022-07, Vol.116 (3), Article 95 |
| issn | 1578-7303 1579-1505 |
| language | eng |
| recordid | cdi_proquest_journals_2648760685 |
| source | SpringerLink Journals |
| subjects | Applications of Mathematics Boundary value problems dedicated to Professor Ildefonso Díaz on the occasion of his 70th birthday Dirichlet problem Mathematical and Computational Physics Mathematics Mathematics and Statistics Original Paper Qualitative Properties of Nonlinear Partial Differential Equations Theoretical |
| title | Lower order terms in divergence form versus lower order terms with natural growth in some Dirichlet problems |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-25T18%3A31%3A36IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Lower%20order%20terms%20in%20divergence%20form%20versus%20lower%20order%20terms%20with%20natural%20growth%20in%20some%20Dirichlet%20problems&rft.jtitle=Revista%20de%20la%20Real%20Academia%20de%20Ciencias%20Exactas,%20F%C3%ADsicas%20y%20Naturales.%20Serie%20A,%20Matem%C3%A1ticas&rft.au=Boccardo,%20Lucio&rft.date=2022-07-01&rft.volume=116&rft.issue=3&rft.artnum=95&rft.issn=1578-7303&rft.eissn=1579-1505&rft_id=info:doi/10.1007/s13398-022-01232-6&rft_dat=%3Cproquest_cross%3E2648760685%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2648760685&rft_id=info:pmid/&rfr_iscdi=true |