Harmonic functions of general graph Laplacians
We study harmonic functions on general weighted graphs which allow for a compatible intrinsic metric. We prove an L p Liouville type theorem which is a quantitative integral L p estimate of harmonic functions analogous to Karp’s theorem for Riemannian manifolds. As corollaries we obtain Yau’s L p -L...
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| Veröffentlicht in: | Calculus of variations and partial differential equations 2014-09, Vol.51 (1-2), p.343-362 |
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| container_title | Calculus of variations and partial differential equations |
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| creator | Hua, Bobo Keller, Matthias |
| description | We study harmonic functions on general weighted graphs which allow for a compatible intrinsic metric. We prove an
L
p
Liouville type theorem which is a quantitative integral
L
p
estimate of harmonic functions analogous to Karp’s theorem for Riemannian manifolds. As corollaries we obtain Yau’s
L
p
-Liouville type theorem on graphs, identify the domain of the generator of the semigroup on
L
p
and get a criterion for recurrence. As a side product, we show an analogue of Yau’s
L
p
Caccioppoli inequality. Furthermore, we derive various Liouville type results for harmonic functions on graphs and harmonic maps from graphs into Hadamard spaces. |
| doi_str_mv | 10.1007/s00526-013-0677-6 |
| format | Article |
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L
p
Liouville type theorem which is a quantitative integral
L
p
estimate of harmonic functions analogous to Karp’s theorem for Riemannian manifolds. As corollaries we obtain Yau’s
L
p
-Liouville type theorem on graphs, identify the domain of the generator of the semigroup on
L
p
and get a criterion for recurrence. As a side product, we show an analogue of Yau’s
L
p
Caccioppoli inequality. Furthermore, we derive various Liouville type results for harmonic functions on graphs and harmonic maps from graphs into Hadamard spaces.</description><identifier>ISSN: 0944-2669</identifier><identifier>EISSN: 1432-0835</identifier><identifier>DOI: 10.1007/s00526-013-0677-6</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Analysis ; Calculus of variations ; Calculus of Variations and Optimal Control; Optimization ; Control ; Criteria ; Estimates ; Generators ; Graph algorithms ; Graphs ; Harmonic analysis ; Harmonic functions ; Harmonics ; Laplace transforms ; Mathematical and Computational Physics ; Mathematical functions ; Mathematics ; Mathematics and Statistics ; Systems Theory ; Texts ; Theorems ; Theoretical</subject><ispartof>Calculus of variations and partial differential equations, 2014-09, Vol.51 (1-2), p.343-362</ispartof><rights>Springer-Verlag Berlin Heidelberg 2013</rights><rights>Springer-Verlag Berlin Heidelberg 2014</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c485t-9ed28a630ff1aca13d50694713a24d2840b299b46277f8230988ab74c9271b323</citedby><cites>FETCH-LOGICAL-c485t-9ed28a630ff1aca13d50694713a24d2840b299b46277f8230988ab74c9271b323</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/s00526-013-0677-6$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00526-013-0677-6$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,777,781,27905,27906,41469,42538,51300</link.rule.ids></links><search><creatorcontrib>Hua, Bobo</creatorcontrib><creatorcontrib>Keller, Matthias</creatorcontrib><title>Harmonic functions of general graph Laplacians</title><title>Calculus of variations and partial differential equations</title><addtitle>Calc. Var</addtitle><description>We study harmonic functions on general weighted graphs which allow for a compatible intrinsic metric. We prove an
L
p
Liouville type theorem which is a quantitative integral
L
p
estimate of harmonic functions analogous to Karp’s theorem for Riemannian manifolds. As corollaries we obtain Yau’s
L
p
-Liouville type theorem on graphs, identify the domain of the generator of the semigroup on
L
p
and get a criterion for recurrence. As a side product, we show an analogue of Yau’s
L
p
Caccioppoli inequality. Furthermore, we derive various Liouville type results for harmonic functions on graphs and harmonic maps from graphs into Hadamard spaces.</description><subject>Analysis</subject><subject>Calculus of variations</subject><subject>Calculus of Variations and Optimal Control; Optimization</subject><subject>Control</subject><subject>Criteria</subject><subject>Estimates</subject><subject>Generators</subject><subject>Graph algorithms</subject><subject>Graphs</subject><subject>Harmonic analysis</subject><subject>Harmonic functions</subject><subject>Harmonics</subject><subject>Laplace transforms</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematical functions</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Systems Theory</subject><subject>Texts</subject><subject>Theorems</subject><subject>Theoretical</subject><issn>0944-2669</issn><issn>1432-0835</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2014</creationdate><recordtype>article</recordtype><recordid>eNp1kD1PwzAQhi0EEqXwA9gisbC4nD_ijxFV0CJVYoHZclynpErtYDcD_x5XYUBILHfDPe_d6UHolsCCAMiHDFBTgYEwDEJKLM7QjHBGMShWn6MZaM4xFUJfoquc9wCkVpTP0GJt0yGGzlXtGNyxiyFXsa12Pvhk-2qX7PBRbezQW9fZkK_RRWv77G9--hy9Pz-9Ldd487p6WT5usOOqPmLtt1RZwaBtiXWWsG0NQnNJmKW8jDg0VOuGCyplqygDrZRtJHeaStIwyubofto7pPg5-nw0hy473_c2-DhmQ2ohQZdKCnr3B93HMYXyXaFqKjUphwtFJsqlmHPyrRlSd7DpyxAwJ4NmMmiKQXMyaETJ0CmTCxt2Pv3a_G_oG3HNcEY</recordid><startdate>20140901</startdate><enddate>20140901</enddate><creator>Hua, Bobo</creator><creator>Keller, Matthias</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>JQ2</scope><scope>7TB</scope><scope>7U5</scope><scope>8FD</scope><scope>FR3</scope><scope>H8D</scope><scope>KR7</scope><scope>L7M</scope></search><sort><creationdate>20140901</creationdate><title>Harmonic functions of general graph Laplacians</title><author>Hua, Bobo ; Keller, Matthias</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c485t-9ed28a630ff1aca13d50694713a24d2840b299b46277f8230988ab74c9271b323</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2014</creationdate><topic>Analysis</topic><topic>Calculus of variations</topic><topic>Calculus of Variations and Optimal Control; Optimization</topic><topic>Control</topic><topic>Criteria</topic><topic>Estimates</topic><topic>Generators</topic><topic>Graph algorithms</topic><topic>Graphs</topic><topic>Harmonic analysis</topic><topic>Harmonic functions</topic><topic>Harmonics</topic><topic>Laplace transforms</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematical functions</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Systems Theory</topic><topic>Texts</topic><topic>Theorems</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Hua, Bobo</creatorcontrib><creatorcontrib>Keller, Matthias</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Computer Science Collection</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>Aerospace Database</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>Calculus of variations and partial differential equations</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Hua, Bobo</au><au>Keller, Matthias</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Harmonic functions of general graph Laplacians</atitle><jtitle>Calculus of variations and partial differential equations</jtitle><stitle>Calc. Var</stitle><date>2014-09-01</date><risdate>2014</risdate><volume>51</volume><issue>1-2</issue><spage>343</spage><epage>362</epage><pages>343-362</pages><issn>0944-2669</issn><eissn>1432-0835</eissn><abstract>We study harmonic functions on general weighted graphs which allow for a compatible intrinsic metric. We prove an
L
p
Liouville type theorem which is a quantitative integral
L
p
estimate of harmonic functions analogous to Karp’s theorem for Riemannian manifolds. As corollaries we obtain Yau’s
L
p
-Liouville type theorem on graphs, identify the domain of the generator of the semigroup on
L
p
and get a criterion for recurrence. As a side product, we show an analogue of Yau’s
L
p
Caccioppoli inequality. Furthermore, we derive various Liouville type results for harmonic functions on graphs and harmonic maps from graphs into Hadamard spaces.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s00526-013-0677-6</doi><tpages>20</tpages></addata></record> |
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| ispartof | Calculus of variations and partial differential equations, 2014-09, Vol.51 (1-2), p.343-362 |
| issn | 0944-2669 1432-0835 |
| language | eng |
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| source | Springer Nature - Complete Springer Journals |
| subjects | Analysis Calculus of variations Calculus of Variations and Optimal Control Optimization Control Criteria Estimates Generators Graph algorithms Graphs Harmonic analysis Harmonic functions Harmonics Laplace transforms Mathematical and Computational Physics Mathematical functions Mathematics Mathematics and Statistics Systems Theory Texts Theorems Theoretical |
| title | Harmonic functions of general graph Laplacians |
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