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Existence of bounded solutions for a class of singular elliptic problems involving the 1-Laplacian operator
In this work we study existence and regularity of solutions to problems which are modeled by - Δ p u + u | ∇ u | p = f h ( u ) in Ω , u = 0 on ∂ Ω . Here Ω is an open bounded subset of R N ( N ≥ 2 ) with Lipschitz boundary, Δ p u : = div ( | ∇ u | p - 2 ∇ u ) ( 1 ≤ p < N ) is the p-Laplacian oper...
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| Published in: | Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas Físicas y Naturales. Serie A, Matemáticas, 2023-07, Vol.117 (3), Article 111 |
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| Language: | English |
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| cites | cdi_FETCH-LOGICAL-c270t-db6236403ce4173c521c099c7f42708c87afc5eb055446d42b1987b07e5e06ee3 |
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| container_issue | 3 |
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| container_title | Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas |
| container_volume | 117 |
| creator | El Hichami, Mohamed El Hadfi, Youssef |
| description | In this work we study existence and regularity of solutions to problems which are modeled by
-
Δ
p
u
+
u
|
∇
u
|
p
=
f
h
(
u
)
in
Ω
,
u
=
0
on
∂
Ω
.
Here
Ω
is an open bounded subset of
R
N
(
N
≥
2
)
with Lipschitz boundary,
Δ
p
u
:
=
div
(
|
∇
u
|
p
-
2
∇
u
)
(
1
≤
p
<
N
)
is the p-Laplacian operator,
f
∈
L
q
(
Ω
)
(
q
>
N
p
)
is a nonnegative function and
h
is a continuous real function that may possibly blow up at zero. |
| doi_str_mv | 10.1007/s13398-023-01444-4 |
| format | article |
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-
Δ
p
u
+
u
|
∇
u
|
p
=
f
h
(
u
)
in
Ω
,
u
=
0
on
∂
Ω
.
Here
Ω
is an open bounded subset of
R
N
(
N
≥
2
)
with Lipschitz boundary,
Δ
p
u
:
=
div
(
|
∇
u
|
p
-
2
∇
u
)
(
1
≤
p
<
N
)
is the p-Laplacian operator,
f
∈
L
q
(
Ω
)
(
q
>
N
p
)
is a nonnegative function and
h
is a continuous real function that may possibly blow up at zero.</description><identifier>ISSN: 1578-7303</identifier><identifier>EISSN: 1579-1505</identifier><identifier>DOI: 10.1007/s13398-023-01444-4</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Applications of Mathematics ; Continuity (mathematics) ; Laplace transforms ; Mathematical and Computational Physics ; Mathematics ; Mathematics and Statistics ; Operators (mathematics) ; Original Paper ; Theoretical</subject><ispartof>Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas, 2023-07, Vol.117 (3), Article 111</ispartof><rights>The Author(s) under exclusive licence to The Royal Academy of Sciences, Madrid 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><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c270t-db6236403ce4173c521c099c7f42708c87afc5eb055446d42b1987b07e5e06ee3</cites><orcidid>0000-0003-4483-2709</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>El Hichami, Mohamed</creatorcontrib><creatorcontrib>El Hadfi, Youssef</creatorcontrib><title>Existence of bounded solutions for a class of singular elliptic problems involving the 1-Laplacian operator</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>In this work we study existence and regularity of solutions to problems which are modeled by
-
Δ
p
u
+
u
|
∇
u
|
p
=
f
h
(
u
)
in
Ω
,
u
=
0
on
∂
Ω
.
Here
Ω
is an open bounded subset of
R
N
(
N
≥
2
)
with Lipschitz boundary,
Δ
p
u
:
=
div
(
|
∇
u
|
p
-
2
∇
u
)
(
1
≤
p
<
N
)
is the p-Laplacian operator,
f
∈
L
q
(
Ω
)
(
q
>
N
p
)
is a nonnegative function and
h
is a continuous real function that may possibly blow up at zero.</description><subject>Applications of Mathematics</subject><subject>Continuity (mathematics)</subject><subject>Laplace transforms</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Operators (mathematics)</subject><subject>Original Paper</subject><subject>Theoretical</subject><issn>1578-7303</issn><issn>1579-1505</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp9UEtLAzEQXkTBUvsHPAU8R5NNttkcpdQHFLzoOWSzszU1TdZkt-i_N-0K3pzLDHyPmfmK4pqSW0qIuEuUMVljUjJMKOcc87NiRishMa1IdX6aaywYYZfFIqUdycUor4mYFR_rL5sG8AZQ6FATRt9Ci1Jw42CDT6gLEWlknE7pSEjWb0enIwLnbD9Yg_oYGgf7hKw_BHfIOBreAVG80b3TxmqPQg9RDyFeFReddgkWv31evD2sX1dPePPy-Ly632BTCjLgtlmWbMkJM8CpYKYqqSFSGtHxjNemFrozFTSkqjhftrxsqKxFQwRUQJYAbF7cTL75ts8R0qB2YYw-r1RlfppJKbjMrHJimRhSitCpPtq9jt-KEnXMVU25qpyrOuWqeBaxSZQy2W8h_ln_o_oBvBF7Ug</recordid><startdate>20230701</startdate><enddate>20230701</enddate><creator>El Hichami, Mohamed</creator><creator>El Hadfi, Youssef</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/0000-0003-4483-2709</orcidid></search><sort><creationdate>20230701</creationdate><title>Existence of bounded solutions for a class of singular elliptic problems involving the 1-Laplacian operator</title><author>El Hichami, Mohamed ; El Hadfi, Youssef</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c270t-db6236403ce4173c521c099c7f42708c87afc5eb055446d42b1987b07e5e06ee3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Applications of Mathematics</topic><topic>Continuity (mathematics)</topic><topic>Laplace transforms</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Operators (mathematics)</topic><topic>Original Paper</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>El Hichami, Mohamed</creatorcontrib><creatorcontrib>El Hadfi, Youssef</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>El Hichami, Mohamed</au><au>El Hadfi, Youssef</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Existence of bounded solutions for a class of singular elliptic problems involving the 1-Laplacian operator</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>2023-07-01</date><risdate>2023</risdate><volume>117</volume><issue>3</issue><artnum>111</artnum><issn>1578-7303</issn><eissn>1579-1505</eissn><abstract>In this work we study existence and regularity of solutions to problems which are modeled by
-
Δ
p
u
+
u
|
∇
u
|
p
=
f
h
(
u
)
in
Ω
,
u
=
0
on
∂
Ω
.
Here
Ω
is an open bounded subset of
R
N
(
N
≥
2
)
with Lipschitz boundary,
Δ
p
u
:
=
div
(
|
∇
u
|
p
-
2
∇
u
)
(
1
≤
p
<
N
)
is the p-Laplacian operator,
f
∈
L
q
(
Ω
)
(
q
>
N
p
)
is a nonnegative function and
h
is a continuous real function that may possibly blow up at zero.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s13398-023-01444-4</doi><orcidid>https://orcid.org/0000-0003-4483-2709</orcidid></addata></record> |
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| identifier | ISSN: 1578-7303 |
| ispartof | Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas, 2023-07, Vol.117 (3), Article 111 |
| issn | 1578-7303 1579-1505 |
| language | eng |
| recordid | cdi_proquest_journals_2807399749 |
| source | Springer Nature |
| subjects | Applications of Mathematics Continuity (mathematics) Laplace transforms Mathematical and Computational Physics Mathematics Mathematics and Statistics Operators (mathematics) Original Paper Theoretical |
| title | Existence of bounded solutions for a class of singular elliptic problems involving the 1-Laplacian operator |
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