Regularity condition by mean oscillation to a weak solution of the 2-dimensional Harmonic heat flow into sphere
We show a regularity criterion to the harmonic heat flow from 2-dimensional Riemannian manifold M into a sphere. It is shown that a weak solution of the harmonic heat flow from 2-dimensional manifold into a sphere is regular under the criterion where BMO r is the space of bounded mean oscillations o...
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| Veröffentlicht in: | Calculus of variations and partial differential equations 2008-12, Vol.33 (4), p.391-415 |
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| container_title | Calculus of variations and partial differential equations |
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| creator | Misawa, Masashi Ogawa, Takayoshi |
| description | We show a regularity criterion to the harmonic heat flow from 2-dimensional Riemannian manifold
M
into a sphere. It is shown that a weak solution of the harmonic heat flow from 2-dimensional manifold into a sphere is regular under the criterion
where
BMO
r
is the space of bounded mean oscillations on
M
. A sharp version of the Sobolev inequality of the Brezis–Gallouet type is introduced on
M
. A monotonicity formula by the mean oscillation is established and applied for proving such a regularity criterion for weak solutions as above. |
| doi_str_mv | 10.1007/s00526-008-0166-5 |
| format | Article |
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M
into a sphere. It is shown that a weak solution of the harmonic heat flow from 2-dimensional manifold into a sphere is regular under the criterion
where
BMO
r
is the space of bounded mean oscillations on
M
. A sharp version of the Sobolev inequality of the Brezis–Gallouet type is introduced on
M
. A monotonicity formula by the mean oscillation is established and applied for proving such a regularity criterion for weak solutions as above.</description><identifier>ISSN: 0944-2669</identifier><identifier>EISSN: 1432-0835</identifier><identifier>DOI: 10.1007/s00526-008-0166-5</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer-Verlag</publisher><subject>Analysis ; Calculus of variations ; Calculus of Variations and Optimal Control; Optimization ; Control ; Criteria ; Harmonics ; Heat transfer ; Heat transmission ; Manifolds ; Mathematical analysis ; Mathematical and Computational Physics ; Mathematics ; Mathematics and Statistics ; Oscillations ; Partial differential equations ; Regularity ; Systems Theory ; Theoretical</subject><ispartof>Calculus of variations and partial differential equations, 2008-12, Vol.33 (4), p.391-415</ispartof><rights>Springer-Verlag 2008</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c379t-2086d035eafb0bd241d6c9a8665ffaf3eb4a5a3a44fdffb7658fa6d0a774d9cd3</citedby><cites>FETCH-LOGICAL-c379t-2086d035eafb0bd241d6c9a8665ffaf3eb4a5a3a44fdffb7658fa6d0a774d9cd3</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/s00526-008-0166-5$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00526-008-0166-5$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Misawa, Masashi</creatorcontrib><creatorcontrib>Ogawa, Takayoshi</creatorcontrib><title>Regularity condition by mean oscillation to a weak solution of the 2-dimensional Harmonic heat flow into sphere</title><title>Calculus of variations and partial differential equations</title><addtitle>Calc. Var</addtitle><description>We show a regularity criterion to the harmonic heat flow from 2-dimensional Riemannian manifold
M
into a sphere. It is shown that a weak solution of the harmonic heat flow from 2-dimensional manifold into a sphere is regular under the criterion
where
BMO
r
is the space of bounded mean oscillations on
M
. A sharp version of the Sobolev inequality of the Brezis–Gallouet type is introduced on
M
. A monotonicity formula by the mean oscillation is established and applied for proving such a regularity criterion for weak solutions as above.</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>Harmonics</subject><subject>Heat transfer</subject><subject>Heat transmission</subject><subject>Manifolds</subject><subject>Mathematical analysis</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Oscillations</subject><subject>Partial differential equations</subject><subject>Regularity</subject><subject>Systems Theory</subject><subject>Theoretical</subject><issn>0944-2669</issn><issn>1432-0835</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2008</creationdate><recordtype>article</recordtype><recordid>eNqNkcFq3DAURUVpoZM0H5Cd6KYrNU-yJMvLMrSZQiBQmrV4tqWMUtuaSDbD_H00mUAgEOjqweWcC49LyCWH7xygvsoASmgGYBhwrZn6QFZcVoKBqdRHsoJGSia0bj6Ts5wfALgyQq5I_OPulwFTmA-0i1Mf5hAn2h7o6HCiMXdhGPA5myNFunf4j-Y4LM9R9HTeOipYH0Y35RLhQDeYxjiFjm4dztQPcU_DVOS827rkvpBPHofsLl7uObn79fPvesNubq9_r3_csK6qm5kJMLqHSjn0LbS9kLzXXYNGa-U9-sq1EhVWKKXvvW9rrYzHYmBdy77p-uqcfDv17lJ8XFye7Rhy58ozk4tLtkYpXcva1P9JVooX8usb8iEuqfycreCN4EoaKBA_QV2KOSfn7S6FEdPBcrDHqexpKlumsseprCqOODm5sNO9S6_F70tP0GWX-A</recordid><startdate>20081201</startdate><enddate>20081201</enddate><creator>Misawa, Masashi</creator><creator>Ogawa, Takayoshi</creator><general>Springer-Verlag</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>20081201</creationdate><title>Regularity condition by mean oscillation to a weak solution of the 2-dimensional Harmonic heat flow into sphere</title><author>Misawa, Masashi ; Ogawa, Takayoshi</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c379t-2086d035eafb0bd241d6c9a8665ffaf3eb4a5a3a44fdffb7658fa6d0a774d9cd3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2008</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>Harmonics</topic><topic>Heat transfer</topic><topic>Heat transmission</topic><topic>Manifolds</topic><topic>Mathematical analysis</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Oscillations</topic><topic>Partial differential equations</topic><topic>Regularity</topic><topic>Systems Theory</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Misawa, Masashi</creatorcontrib><creatorcontrib>Ogawa, Takayoshi</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>Misawa, Masashi</au><au>Ogawa, Takayoshi</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Regularity condition by mean oscillation to a weak solution of the 2-dimensional Harmonic heat flow into sphere</atitle><jtitle>Calculus of variations and partial differential equations</jtitle><stitle>Calc. Var</stitle><date>2008-12-01</date><risdate>2008</risdate><volume>33</volume><issue>4</issue><spage>391</spage><epage>415</epage><pages>391-415</pages><issn>0944-2669</issn><eissn>1432-0835</eissn><abstract>We show a regularity criterion to the harmonic heat flow from 2-dimensional Riemannian manifold
M
into a sphere. It is shown that a weak solution of the harmonic heat flow from 2-dimensional manifold into a sphere is regular under the criterion
where
BMO
r
is the space of bounded mean oscillations on
M
. A sharp version of the Sobolev inequality of the Brezis–Gallouet type is introduced on
M
. A monotonicity formula by the mean oscillation is established and applied for proving such a regularity criterion for weak solutions as above.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer-Verlag</pub><doi>10.1007/s00526-008-0166-5</doi><tpages>25</tpages></addata></record> |
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| ispartof | Calculus of variations and partial differential equations, 2008-12, Vol.33 (4), p.391-415 |
| issn | 0944-2669 1432-0835 |
| language | eng |
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| source | SpringerLink Journals |
| subjects | Analysis Calculus of variations Calculus of Variations and Optimal Control Optimization Control Criteria Harmonics Heat transfer Heat transmission Manifolds Mathematical analysis Mathematical and Computational Physics Mathematics Mathematics and Statistics Oscillations Partial differential equations Regularity Systems Theory Theoretical |
| title | Regularity condition by mean oscillation to a weak solution of the 2-dimensional Harmonic heat flow into sphere |
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