The Hardy inequality and nonlinear parabolic equations on Carnot groups
In this paper we shall investigate the nonexistence of positive solutions for the following nonlinear parabolic partial differential equation: { ∂ u ∂ t = Δ G , p u + V ( x ) u p − 1 in Ω × ( 0 , T ) , 1 < p < 2 , u ( x , 0 ) = u 0 ( x ) ≥ 0 in Ω , u ( x , t ) = 0 on ∂ Ω × ( 0 , T ) , where Δ...
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| Veröffentlicht in: | Nonlinear analysis 2008-12, Vol.69 (12), p.4643-4653 |
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| container_title | Nonlinear analysis |
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| creator | Goldstein, Jerome A. Kombe, Ismail |
| description | In this paper we shall investigate the nonexistence of positive solutions for the following nonlinear parabolic partial differential equation:
{
∂
u
∂
t
=
Δ
G
,
p
u
+
V
(
x
)
u
p
−
1
in
Ω
×
(
0
,
T
)
,
1
<
p
<
2
,
u
(
x
,
0
)
=
u
0
(
x
)
≥
0
in
Ω
,
u
(
x
,
t
)
=
0
on
∂
Ω
×
(
0
,
T
)
,
where
Δ
G
,
p
is the
p
-sub-Laplacian on a Carnot group
G
and
V
∈
L
loc
1
(
Ω
)
. |
| doi_str_mv | 10.1016/j.na.2007.11.020 |
| format | Article |
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{
∂
u
∂
t
=
Δ
G
,
p
u
+
V
(
x
)
u
p
−
1
in
Ω
×
(
0
,
T
)
,
1
<
p
<
2
,
u
(
x
,
0
)
=
u
0
(
x
)
≥
0
in
Ω
,
u
(
x
,
t
)
=
0
on
∂
Ω
×
(
0
,
T
)
,
where
Δ
G
,
p
is the
p
-sub-Laplacian on a Carnot group
G
and
V
∈
L
loc
1
(
Ω
)
.</description><identifier>ISSN: 0362-546X</identifier><identifier>EISSN: 1873-5215</identifier><identifier>DOI: 10.1016/j.na.2007.11.020</identifier><identifier>CODEN: NOANDD</identifier><language>eng</language><publisher>Amsterdam: Elsevier Ltd</publisher><subject>Exact sciences and technology ; Hardy-type inequality ; Mathematical analysis ; Mathematics ; Nonlinear parabolic equations ; Numerical analysis ; Numerical analysis. Scientific computation ; Partial differential equations ; Partial differential equations, boundary value problems ; Partial differential equations, initial value problems and time-dependant initial-boundary value problems ; Positive solutions ; Sciences and techniques of general use</subject><ispartof>Nonlinear analysis, 2008-12, Vol.69 (12), p.4643-4653</ispartof><rights>2007 Elsevier Ltd</rights><rights>2015 INIST-CNRS</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c463t-a2f942ded0ce036434f831a8d95f10491233b934ce326160b70296da64d3b8993</citedby><cites>FETCH-LOGICAL-c463t-a2f942ded0ce036434f831a8d95f10491233b934ce326160b70296da64d3b8993</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.na.2007.11.020$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,777,781,3537,27905,27906,45976</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=20894239$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Goldstein, Jerome A.</creatorcontrib><creatorcontrib>Kombe, Ismail</creatorcontrib><title>The Hardy inequality and nonlinear parabolic equations on Carnot groups</title><title>Nonlinear analysis</title><description>In this paper we shall investigate the nonexistence of positive solutions for the following nonlinear parabolic partial differential equation:
{
∂
u
∂
t
=
Δ
G
,
p
u
+
V
(
x
)
u
p
−
1
in
Ω
×
(
0
,
T
)
,
1
<
p
<
2
,
u
(
x
,
0
)
=
u
0
(
x
)
≥
0
in
Ω
,
u
(
x
,
t
)
=
0
on
∂
Ω
×
(
0
,
T
)
,
where
Δ
G
,
p
is the
p
-sub-Laplacian on a Carnot group
G
and
V
∈
L
loc
1
(
Ω
)
.</description><subject>Exact sciences and technology</subject><subject>Hardy-type inequality</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Nonlinear parabolic equations</subject><subject>Numerical analysis</subject><subject>Numerical analysis. Scientific computation</subject><subject>Partial differential equations</subject><subject>Partial differential equations, boundary value problems</subject><subject>Partial differential equations, initial value problems and time-dependant initial-boundary value problems</subject><subject>Positive solutions</subject><subject>Sciences and techniques of general use</subject><issn>0362-546X</issn><issn>1873-5215</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2008</creationdate><recordtype>article</recordtype><recordid>eNp1kDFPwzAQhS0EEqWwM3qBLeFsJ07ChipokSqxFInNutoOuErt1E6R-u9JVcTGdNLpe-_ePUJuGeQMmHzY5B5zDlDljOXA4YxMWF2JrOSsPCcTEJJnZSE_LslVShsAYJWQEzJffVm6wGgO1Hm722PnhgNFb6gPvhtXGGmPEdehc5oegcEFn2jwdIbRh4F-xrDv0zW5aLFL9uZ3Tsn7y_NqtsiWb_PX2dMy04UUQ4a8bQpurAFtx0iFKNpaMKxNU7YMioZxIdaNKLQVXDIJ6wp4Iw3Kwoh13TRiSu5Pvn0Mu71Ng9q6pG3Xobdhn5QoZd1IECMIJ1DHkFK0reqj22I8KAbq2JjaKI_q2JhiTI2NjZK7X29MGrs2otcu_ek41GN2cczweOLs-Oi3s1El7azX1rho9aBMcP8f-QH7on7j</recordid><startdate>20081215</startdate><enddate>20081215</enddate><creator>Goldstein, Jerome A.</creator><creator>Kombe, Ismail</creator><general>Elsevier Ltd</general><general>Elsevier</general><scope>IQODW</scope><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></search><sort><creationdate>20081215</creationdate><title>The Hardy inequality and nonlinear parabolic equations on Carnot groups</title><author>Goldstein, Jerome A. ; Kombe, Ismail</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c463t-a2f942ded0ce036434f831a8d95f10491233b934ce326160b70296da64d3b8993</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2008</creationdate><topic>Exact sciences and technology</topic><topic>Hardy-type inequality</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Nonlinear parabolic equations</topic><topic>Numerical analysis</topic><topic>Numerical analysis. Scientific computation</topic><topic>Partial differential equations</topic><topic>Partial differential equations, boundary value problems</topic><topic>Partial differential equations, initial value problems and time-dependant initial-boundary value problems</topic><topic>Positive solutions</topic><topic>Sciences and techniques of general use</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Goldstein, Jerome A.</creatorcontrib><creatorcontrib>Kombe, Ismail</creatorcontrib><collection>Pascal-Francis</collection><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>Nonlinear analysis</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Goldstein, Jerome A.</au><au>Kombe, Ismail</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The Hardy inequality and nonlinear parabolic equations on Carnot groups</atitle><jtitle>Nonlinear analysis</jtitle><date>2008-12-15</date><risdate>2008</risdate><volume>69</volume><issue>12</issue><spage>4643</spage><epage>4653</epage><pages>4643-4653</pages><issn>0362-546X</issn><eissn>1873-5215</eissn><coden>NOANDD</coden><abstract>In this paper we shall investigate the nonexistence of positive solutions for the following nonlinear parabolic partial differential equation:
{
∂
u
∂
t
=
Δ
G
,
p
u
+
V
(
x
)
u
p
−
1
in
Ω
×
(
0
,
T
)
,
1
<
p
<
2
,
u
(
x
,
0
)
=
u
0
(
x
)
≥
0
in
Ω
,
u
(
x
,
t
)
=
0
on
∂
Ω
×
(
0
,
T
)
,
where
Δ
G
,
p
is the
p
-sub-Laplacian on a Carnot group
G
and
V
∈
L
loc
1
(
Ω
)
.</abstract><cop>Amsterdam</cop><pub>Elsevier Ltd</pub><doi>10.1016/j.na.2007.11.020</doi><tpages>11</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0362-546X |
| ispartof | Nonlinear analysis, 2008-12, Vol.69 (12), p.4643-4653 |
| issn | 0362-546X 1873-5215 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_35689603 |
| source | Elsevier ScienceDirect Journals |
| subjects | Exact sciences and technology Hardy-type inequality Mathematical analysis Mathematics Nonlinear parabolic equations Numerical analysis Numerical analysis. Scientific computation Partial differential equations Partial differential equations, boundary value problems Partial differential equations, initial value problems and time-dependant initial-boundary value problems Positive solutions Sciences and techniques of general use |
| title | The Hardy inequality and nonlinear parabolic equations on Carnot groups |
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