Gradient estimates for some f-heat equations driven by Lichnerowicz’s equation on complete smooth metric measure spaces
Given a complete, smooth metric measure space ( M , g , e - f d v ) with the Bakry–Émery Ricci curvature bounded from below, various gradient estimates for solutions of the following general f -heat equations u t = Δ f u + a u log u + b u + A u p + B u - q and u t = Δ f u + A e p u + B e - p u + D a...
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| Veröffentlicht in: | Manuscripta mathematica 2018-03, Vol.155 (3-4), p.471-501 |
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| container_title | Manuscripta mathematica |
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| creator | Dung, Nguyen Thac Khanh, Nguyen Ngoc Ngô, Quốc Anh |
| description | Given a complete, smooth metric measure space
(
M
,
g
,
e
-
f
d
v
)
with the Bakry–Émery Ricci curvature bounded from below, various gradient estimates for solutions of the following general
f
-heat equations
u
t
=
Δ
f
u
+
a
u
log
u
+
b
u
+
A
u
p
+
B
u
-
q
and
u
t
=
Δ
f
u
+
A
e
p
u
+
B
e
-
p
u
+
D
are studied. As by-product, we obtain some Liouville-type theorems and Harnack-type inequalities for positive solutions of several nonlinear equations including the Schrödinger equation, the Yamabe equation, and Lichnerowicz-type equations as special cases. |
| doi_str_mv | 10.1007/s00229-017-0946-3 |
| format | Article |
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(
M
,
g
,
e
-
f
d
v
)
with the Bakry–Émery Ricci curvature bounded from below, various gradient estimates for solutions of the following general
f
-heat equations
u
t
=
Δ
f
u
+
a
u
log
u
+
b
u
+
A
u
p
+
B
u
-
q
and
u
t
=
Δ
f
u
+
A
e
p
u
+
B
e
-
p
u
+
D
are studied. As by-product, we obtain some Liouville-type theorems and Harnack-type inequalities for positive solutions of several nonlinear equations including the Schrödinger equation, the Yamabe equation, and Lichnerowicz-type equations as special cases.</description><identifier>ISSN: 0025-2611</identifier><identifier>EISSN: 1432-1785</identifier><identifier>DOI: 10.1007/s00229-017-0946-3</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Algebraic Geometry ; Calculus of Variations and Optimal Control; Optimization ; Curvature ; Geometry ; Lie Groups ; Mathematical analysis ; Mathematics ; Mathematics and Statistics ; Nonlinear equations ; Number Theory ; Schrodinger equation ; Thermodynamics ; Topological Groups</subject><ispartof>Manuscripta mathematica, 2018-03, Vol.155 (3-4), p.471-501</ispartof><rights>Springer-Verlag GmbH Germany 2017</rights><rights>Copyright Springer Science & Business Media 2018</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c316t-2785ad14324471089b499766142e669d5750b0e8c22487b508ff7536b94c9ba93</citedby><cites>FETCH-LOGICAL-c316t-2785ad14324471089b499766142e669d5750b0e8c22487b508ff7536b94c9ba93</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/s00229-017-0946-3$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00229-017-0946-3$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Dung, Nguyen Thac</creatorcontrib><creatorcontrib>Khanh, Nguyen Ngoc</creatorcontrib><creatorcontrib>Ngô, Quốc Anh</creatorcontrib><title>Gradient estimates for some f-heat equations driven by Lichnerowicz’s equation on complete smooth metric measure spaces</title><title>Manuscripta mathematica</title><addtitle>manuscripta math</addtitle><description>Given a complete, smooth metric measure space
(
M
,
g
,
e
-
f
d
v
)
with the Bakry–Émery Ricci curvature bounded from below, various gradient estimates for solutions of the following general
f
-heat equations
u
t
=
Δ
f
u
+
a
u
log
u
+
b
u
+
A
u
p
+
B
u
-
q
and
u
t
=
Δ
f
u
+
A
e
p
u
+
B
e
-
p
u
+
D
are studied. As by-product, we obtain some Liouville-type theorems and Harnack-type inequalities for positive solutions of several nonlinear equations including the Schrödinger equation, the Yamabe equation, and Lichnerowicz-type equations as special cases.</description><subject>Algebraic Geometry</subject><subject>Calculus of Variations and Optimal Control; Optimization</subject><subject>Curvature</subject><subject>Geometry</subject><subject>Lie Groups</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Nonlinear equations</subject><subject>Number Theory</subject><subject>Schrodinger equation</subject><subject>Thermodynamics</subject><subject>Topological Groups</subject><issn>0025-2611</issn><issn>1432-1785</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><recordid>eNp1kM1KxDAUhYMoOI4-gLuA62iSpk2zlME_GHCj65Cmt06HadNJMsq48jV8PZ_ElIquhIQLOefcm_shdM7oJaNUXgVKOVeEMkmoEgXJDtCMiYwTJsv8EM2SnBNeMHaMTkJYU5pEmc3Q_s6buoU-Ygix7UyEgBvncXAd4IaswCRluzOxdX3AtW9focfVHi9bu-rBu7fWvn99fIZfE07Hum7YQAQcOufiCncQfWtTMWHn0-tgLIRTdNSYTYCznzpHz7c3T4t7sny8e1hcL4nNWBEJT_839biKEJLRUlVCKVkUTHAoClXnMqcVhdJyLkpZ5bRsGplnRaWEVZVR2RxdTH0H77a7tKVeu53v00jNExWarsqSi00u610IHho9-ITD7zWjeiSsJ8I6EdYjYT1m-JQJydu_gP_r_H_oG1Gwf5k</recordid><startdate>20180301</startdate><enddate>20180301</enddate><creator>Dung, Nguyen Thac</creator><creator>Khanh, Nguyen Ngoc</creator><creator>Ngô, Quốc Anh</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20180301</creationdate><title>Gradient estimates for some f-heat equations driven by Lichnerowicz’s equation on complete smooth metric measure spaces</title><author>Dung, Nguyen Thac ; Khanh, Nguyen Ngoc ; Ngô, Quốc Anh</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c316t-2785ad14324471089b499766142e669d5750b0e8c22487b508ff7536b94c9ba93</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Algebraic Geometry</topic><topic>Calculus of Variations and Optimal Control; Optimization</topic><topic>Curvature</topic><topic>Geometry</topic><topic>Lie Groups</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Nonlinear equations</topic><topic>Number Theory</topic><topic>Schrodinger equation</topic><topic>Thermodynamics</topic><topic>Topological Groups</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Dung, Nguyen Thac</creatorcontrib><creatorcontrib>Khanh, Nguyen Ngoc</creatorcontrib><creatorcontrib>Ngô, Quốc Anh</creatorcontrib><collection>CrossRef</collection><jtitle>Manuscripta mathematica</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Dung, Nguyen Thac</au><au>Khanh, Nguyen Ngoc</au><au>Ngô, Quốc Anh</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Gradient estimates for some f-heat equations driven by Lichnerowicz’s equation on complete smooth metric measure spaces</atitle><jtitle>Manuscripta mathematica</jtitle><stitle>manuscripta math</stitle><date>2018-03-01</date><risdate>2018</risdate><volume>155</volume><issue>3-4</issue><spage>471</spage><epage>501</epage><pages>471-501</pages><issn>0025-2611</issn><eissn>1432-1785</eissn><abstract>Given a complete, smooth metric measure space
(
M
,
g
,
e
-
f
d
v
)
with the Bakry–Émery Ricci curvature bounded from below, various gradient estimates for solutions of the following general
f
-heat equations
u
t
=
Δ
f
u
+
a
u
log
u
+
b
u
+
A
u
p
+
B
u
-
q
and
u
t
=
Δ
f
u
+
A
e
p
u
+
B
e
-
p
u
+
D
are studied. As by-product, we obtain some Liouville-type theorems and Harnack-type inequalities for positive solutions of several nonlinear equations including the Schrödinger equation, the Yamabe equation, and Lichnerowicz-type equations as special cases.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s00229-017-0946-3</doi><tpages>31</tpages></addata></record> |
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| ispartof | Manuscripta mathematica, 2018-03, Vol.155 (3-4), p.471-501 |
| issn | 0025-2611 1432-1785 |
| language | eng |
| recordid | cdi_proquest_journals_2002000293 |
| source | SpringerLink Journals - AutoHoldings |
| subjects | Algebraic Geometry Calculus of Variations and Optimal Control Optimization Curvature Geometry Lie Groups Mathematical analysis Mathematics Mathematics and Statistics Nonlinear equations Number Theory Schrodinger equation Thermodynamics Topological Groups |
| title | Gradient estimates for some f-heat equations driven by Lichnerowicz’s equation on complete smooth metric measure spaces |
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