Anisotropic degenerate elliptic problem with singular gradient lower order term
In this paper, we investigate the existence and regularity results of anisotropic elliptic equations with degenerate coercivity and a singular lower order term exhibiting natural growth with respect to the gradient. The model problem we consider is 0.1 - ∑ i = 1 N D i [ | D i u | p i - 2 D i u ( 1 +...
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| Veröffentlicht in: | Bollettino della Unione matematica italiana (2008) 2024-03, Vol.17 (1), p.149-174 |
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| creator | Khelifi, Hichem |
| description | In this paper, we investigate the existence and regularity results of anisotropic elliptic equations with degenerate coercivity and a singular lower order term exhibiting natural growth with respect to the gradient. The model problem we consider is
0.1
-
∑
i
=
1
N
D
i
[
|
D
i
u
|
p
i
-
2
D
i
u
(
1
+
|
u
|
)
γ
]
+
∑
i
=
1
N
|
D
i
u
|
p
i
|
u
|
θ
=
f
in
Ω
,
u
=
0
on
∂
Ω
,
where
Ω
is a bounded domain in
R
N
,
γ
>
0
,
0
≤
θ
<
1
and
2
≤
p
1
≤
p
2
≤
⋯
≤
p
N
. The results of our study will rely on the summability of
f
in specific Lebesgue spaces and the value of
γ
. |
| doi_str_mv | 10.1007/s40574-023-00395-3 |
| format | Article |
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0.1
-
∑
i
=
1
N
D
i
[
|
D
i
u
|
p
i
-
2
D
i
u
(
1
+
|
u
|
)
γ
]
+
∑
i
=
1
N
|
D
i
u
|
p
i
|
u
|
θ
=
f
in
Ω
,
u
=
0
on
∂
Ω
,
where
Ω
is a bounded domain in
R
N
,
γ
>
0
,
0
≤
θ
<
1
and
2
≤
p
1
≤
p
2
≤
⋯
≤
p
N
. The results of our study will rely on the summability of
f
in specific Lebesgue spaces and the value of
γ
.</description><identifier>ISSN: 1972-6724</identifier><identifier>EISSN: 2198-2759</identifier><identifier>DOI: 10.1007/s40574-023-00395-3</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Coercivity ; Elliptic functions ; Mathematics ; Mathematics and Statistics</subject><ispartof>Bollettino della Unione matematica italiana (2008), 2024-03, Vol.17 (1), p.149-174</ispartof><rights>The Author(s), under exclusive licence to Unione Matematica Italiana 2023. 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><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-c5de6efa613030cf86f7871169db4498f35e74533168537f6026713d1b10dcfc3</citedby><cites>FETCH-LOGICAL-c319t-c5de6efa613030cf86f7871169db4498f35e74533168537f6026713d1b10dcfc3</cites><orcidid>0000-0001-5070-9999</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/s40574-023-00395-3$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s40574-023-00395-3$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27923,27924,41487,42556,51318</link.rule.ids></links><search><creatorcontrib>Khelifi, Hichem</creatorcontrib><title>Anisotropic degenerate elliptic problem with singular gradient lower order term</title><title>Bollettino della Unione matematica italiana (2008)</title><addtitle>Boll Unione Mat Ital</addtitle><description>In this paper, we investigate the existence and regularity results of anisotropic elliptic equations with degenerate coercivity and a singular lower order term exhibiting natural growth with respect to the gradient. The model problem we consider is
0.1
-
∑
i
=
1
N
D
i
[
|
D
i
u
|
p
i
-
2
D
i
u
(
1
+
|
u
|
)
γ
]
+
∑
i
=
1
N
|
D
i
u
|
p
i
|
u
|
θ
=
f
in
Ω
,
u
=
0
on
∂
Ω
,
where
Ω
is a bounded domain in
R
N
,
γ
>
0
,
0
≤
θ
<
1
and
2
≤
p
1
≤
p
2
≤
⋯
≤
p
N
. The results of our study will rely on the summability of
f
in specific Lebesgue spaces and the value of
γ
.</description><subject>Coercivity</subject><subject>Elliptic functions</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><issn>1972-6724</issn><issn>2198-2759</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><recordid>eNp9kE9LxDAQxYMouKz7BTwVPEdnkjZpjsviPxD2oufQbSe1S7etSZbFb2-0gjcvMzC89-bxY-wa4RYB9F3IodA5ByE5gDQFl2dsIdCUXOjCnLMFGi240iK_ZKsQ9gCAKEtt9IJt10MXxujHqauzhloayFeRMur7borpNvlx19MhO3XxPQvd0B77ymetr5qOhpj144l8NvomzUj-cMUuXNUHWv3uJXt7uH_dPPGX7ePzZv3Ca4km8rpoSJGrFEqQULtSOV1qRGWaXZ6b0smCdF5IiaospHYKhNIoG9whNLWr5ZLdzLmp38eRQrT78eiH9NIKI3KNSgmdVGJW1X4MwZOzk-8Olf-0CPabnZ3Z2cTO_rCzMpnkbApJPLTk_6L_cX0BHtNxZg</recordid><startdate>20240301</startdate><enddate>20240301</enddate><creator>Khelifi, Hichem</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0001-5070-9999</orcidid></search><sort><creationdate>20240301</creationdate><title>Anisotropic degenerate elliptic problem with singular gradient lower order term</title><author>Khelifi, Hichem</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-c5de6efa613030cf86f7871169db4498f35e74533168537f6026713d1b10dcfc3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Coercivity</topic><topic>Elliptic functions</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><toplevel>online_resources</toplevel><creatorcontrib>Khelifi, Hichem</creatorcontrib><collection>CrossRef</collection><jtitle>Bollettino della Unione matematica italiana (2008)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Khelifi, Hichem</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Anisotropic degenerate elliptic problem with singular gradient lower order term</atitle><jtitle>Bollettino della Unione matematica italiana (2008)</jtitle><stitle>Boll Unione Mat Ital</stitle><date>2024-03-01</date><risdate>2024</risdate><volume>17</volume><issue>1</issue><spage>149</spage><epage>174</epage><pages>149-174</pages><issn>1972-6724</issn><eissn>2198-2759</eissn><abstract>In this paper, we investigate the existence and regularity results of anisotropic elliptic equations with degenerate coercivity and a singular lower order term exhibiting natural growth with respect to the gradient. The model problem we consider is
0.1
-
∑
i
=
1
N
D
i
[
|
D
i
u
|
p
i
-
2
D
i
u
(
1
+
|
u
|
)
γ
]
+
∑
i
=
1
N
|
D
i
u
|
p
i
|
u
|
θ
=
f
in
Ω
,
u
=
0
on
∂
Ω
,
where
Ω
is a bounded domain in
R
N
,
γ
>
0
,
0
≤
θ
<
1
and
2
≤
p
1
≤
p
2
≤
⋯
≤
p
N
. The results of our study will rely on the summability of
f
in specific Lebesgue spaces and the value of
γ
.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s40574-023-00395-3</doi><tpages>26</tpages><orcidid>https://orcid.org/0000-0001-5070-9999</orcidid></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1972-6724 |
| ispartof | Bollettino della Unione matematica italiana (2008), 2024-03, Vol.17 (1), p.149-174 |
| issn | 1972-6724 2198-2759 |
| language | eng |
| recordid | cdi_proquest_journals_2924716627 |
| source | SpringerLink Journals - AutoHoldings |
| subjects | Coercivity Elliptic functions Mathematics Mathematics and Statistics |
| title | Anisotropic degenerate elliptic problem with singular gradient lower order term |
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