Averaging lemmas with a force term in the transport equation
We obtain several averaging lemmas for transport operator with a force term. These lemmas improve the regularity yet known by not considering the force term as part of an arbitrary right-hand side. Two methods are used: local variable changes or stationary phase. These new results are subjected to t...
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| Veröffentlicht in: | Journal de mathématiques pures et appliquées 2010-02, Vol.93 (2), p.113-131 |
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| creator | Berthelin, F. Junca, S. |
| description | We obtain several averaging lemmas for transport operator with a force term. These lemmas improve the regularity yet known by not considering the force term as part of an arbitrary right-hand side. Two methods are used: local variable changes or stationary phase. These new results are subjected to two non-degeneracy assumptions. We characterize the optimal conditions of these assumptions to compare the obtained regularities according to the space and velocity variables. Our results are mainly in
L
2
, and for constant force, in
L
p
for
1
<
p
⩽
2
.
Nous obtenons plusieurs lemmes de moyenne pour des équations de transport avec un terme de force. Ces résultats améliorent la régularité connue en ne considérant pas le terme de force comme terme source arbitraire. Deux techniques sont utilisées : des changements de variables locaux ou des phases stationnaires. Ces résultats sont quantifiées par deux hypothèses de non dégénérescence. Nous caractérisons les conditions optimales de ces hypothèses pour comparer les régularités obtenues, par rapport aux variables d'espace et de vitesse. Les résultats sont principalement dans
L
2
, et pour le cas constant, dans
L
p
pour
1
<
p
⩽
2
. |
| doi_str_mv | 10.1016/j.matpur.2009.10.009 |
| format | Article |
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L
2
, and for constant force, in
L
p
for
1
<
p
⩽
2
.
Nous obtenons plusieurs lemmes de moyenne pour des équations de transport avec un terme de force. Ces résultats améliorent la régularité connue en ne considérant pas le terme de force comme terme source arbitraire. Deux techniques sont utilisées : des changements de variables locaux ou des phases stationnaires. Ces résultats sont quantifiées par deux hypothèses de non dégénérescence. Nous caractérisons les conditions optimales de ces hypothèses pour comparer les régularités obtenues, par rapport aux variables d'espace et de vitesse. Les résultats sont principalement dans
L
2
, et pour le cas constant, dans
L
p
pour
1
<
p
⩽
2
.</description><identifier>ISSN: 0021-7824</identifier><identifier>DOI: 10.1016/j.matpur.2009.10.009</identifier><identifier>CODEN: JMPAAM</identifier><language>eng</language><publisher>Kidlington: Elsevier SAS</publisher><subject>Analysis of PDEs ; Averaging lemma ; Exact sciences and technology ; Force term ; Fourier analysis ; Fourier series ; General mathematics ; General, history and biography ; Hardy space ; Kinetic equation ; Mathematical analysis ; Mathematics ; Non-degeneracy conditions ; Sciences and techniques of general use ; Stationary phase</subject><ispartof>Journal de mathématiques pures et appliquées, 2010-02, Vol.93 (2), p.113-131</ispartof><rights>2009 Elsevier Masson SAS</rights><rights>2015 INIST-CNRS</rights><rights>Distributed under a Creative Commons Attribution 4.0 International License</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c370t-5dc5d35e1705ccb1eee16d0f506985e4f18a03d5c53d12317075d894cedd94783</citedby><cites>FETCH-LOGICAL-c370t-5dc5d35e1705ccb1eee16d0f506985e4f18a03d5c53d12317075d894cedd94783</cites><orcidid>0000-0003-0445-255X</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.matpur.2009.10.009$$EHTML$$P50$$Gelsevier$$Hfree_for_read</linktohtml><link.rule.ids>230,314,780,784,885,3548,27923,27924,45994</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=22375126$$DView record in Pascal Francis$$Hfree_for_read</backlink><backlink>$$Uhttps://hal.science/hal-00874401$$DView record in HAL$$Hfree_for_read</backlink></links><search><creatorcontrib>Berthelin, F.</creatorcontrib><creatorcontrib>Junca, S.</creatorcontrib><title>Averaging lemmas with a force term in the transport equation</title><title>Journal de mathématiques pures et appliquées</title><description>We obtain several averaging lemmas for transport operator with a force term. These lemmas improve the regularity yet known by not considering the force term as part of an arbitrary right-hand side. Two methods are used: local variable changes or stationary phase. These new results are subjected to two non-degeneracy assumptions. We characterize the optimal conditions of these assumptions to compare the obtained regularities according to the space and velocity variables. Our results are mainly in
L
2
, and for constant force, in
L
p
for
1
<
p
⩽
2
.
Nous obtenons plusieurs lemmes de moyenne pour des équations de transport avec un terme de force. Ces résultats améliorent la régularité connue en ne considérant pas le terme de force comme terme source arbitraire. Deux techniques sont utilisées : des changements de variables locaux ou des phases stationnaires. Ces résultats sont quantifiées par deux hypothèses de non dégénérescence. Nous caractérisons les conditions optimales de ces hypothèses pour comparer les régularités obtenues, par rapport aux variables d'espace et de vitesse. Les résultats sont principalement dans
L
2
, et pour le cas constant, dans
L
p
pour
1
<
p
⩽
2
.</description><subject>Analysis of PDEs</subject><subject>Averaging lemma</subject><subject>Exact sciences and technology</subject><subject>Force term</subject><subject>Fourier analysis</subject><subject>Fourier series</subject><subject>General mathematics</subject><subject>General, history and biography</subject><subject>Hardy space</subject><subject>Kinetic equation</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Non-degeneracy conditions</subject><subject>Sciences and techniques of general use</subject><subject>Stationary phase</subject><issn>0021-7824</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2010</creationdate><recordtype>article</recordtype><recordid>eNp9kDtPwzAUhT2ARCn8AwYvDAwJ10mch4SQqgooUiUWmC1j37Su8sJ2g_j3OArqiJdjHX3H1_cQcsMgZsDy-0PcSj8cbZwAVMGKg5yRBUDCoqJMsgty6dwBwqnyfEEeViNauTPdjjbYttLRb-P3VNK6twqpR9tS01G_D3crOzf01lP8Okpv-u6KnNeycXj9p0vy8fz0vt5E27eX1_VqG6m0AB9xrbhOObICuFKfDBFZrqHmkFclx6xmpYRUc8VTzZI0YAXXZZUp1LrKijJdkrv53b1sxGBNK-2P6KURm9VWTB5AWWQZsJEFNptZZXvnLNanAAMxNSQOYm5ITA1NbpAQu51jg3RKNnXYVRl3yiZJWnCW5IF7nDkM-44GrXDKYBe-aiwqL3Rv_h_0C8DFfvY</recordid><startdate>20100201</startdate><enddate>20100201</enddate><creator>Berthelin, F.</creator><creator>Junca, S.</creator><general>Elsevier SAS</general><general>Elsevier</general><scope>6I.</scope><scope>AAFTH</scope><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>1XC</scope><scope>VOOES</scope><orcidid>https://orcid.org/0000-0003-0445-255X</orcidid></search><sort><creationdate>20100201</creationdate><title>Averaging lemmas with a force term in the transport equation</title><author>Berthelin, F. ; Junca, S.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c370t-5dc5d35e1705ccb1eee16d0f506985e4f18a03d5c53d12317075d894cedd94783</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2010</creationdate><topic>Analysis of PDEs</topic><topic>Averaging lemma</topic><topic>Exact sciences and technology</topic><topic>Force term</topic><topic>Fourier analysis</topic><topic>Fourier series</topic><topic>General mathematics</topic><topic>General, history and biography</topic><topic>Hardy space</topic><topic>Kinetic equation</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Non-degeneracy conditions</topic><topic>Sciences and techniques of general use</topic><topic>Stationary phase</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Berthelin, F.</creatorcontrib><creatorcontrib>Junca, S.</creatorcontrib><collection>ScienceDirect Open Access Titles</collection><collection>Elsevier:ScienceDirect:Open Access</collection><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Hyper Article en Ligne (HAL)</collection><collection>Hyper Article en Ligne (HAL) (Open Access)</collection><jtitle>Journal de mathématiques pures et appliquées</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Berthelin, F.</au><au>Junca, S.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Averaging lemmas with a force term in the transport equation</atitle><jtitle>Journal de mathématiques pures et appliquées</jtitle><date>2010-02-01</date><risdate>2010</risdate><volume>93</volume><issue>2</issue><spage>113</spage><epage>131</epage><pages>113-131</pages><issn>0021-7824</issn><coden>JMPAAM</coden><abstract>We obtain several averaging lemmas for transport operator with a force term. These lemmas improve the regularity yet known by not considering the force term as part of an arbitrary right-hand side. Two methods are used: local variable changes or stationary phase. These new results are subjected to two non-degeneracy assumptions. We characterize the optimal conditions of these assumptions to compare the obtained regularities according to the space and velocity variables. Our results are mainly in
L
2
, and for constant force, in
L
p
for
1
<
p
⩽
2
.
Nous obtenons plusieurs lemmes de moyenne pour des équations de transport avec un terme de force. Ces résultats améliorent la régularité connue en ne considérant pas le terme de force comme terme source arbitraire. Deux techniques sont utilisées : des changements de variables locaux ou des phases stationnaires. Ces résultats sont quantifiées par deux hypothèses de non dégénérescence. Nous caractérisons les conditions optimales de ces hypothèses pour comparer les régularités obtenues, par rapport aux variables d'espace et de vitesse. Les résultats sont principalement dans
L
2
, et pour le cas constant, dans
L
p
pour
1
<
p
⩽
2
.</abstract><cop>Kidlington</cop><pub>Elsevier SAS</pub><doi>10.1016/j.matpur.2009.10.009</doi><tpages>19</tpages><orcidid>https://orcid.org/0000-0003-0445-255X</orcidid><oa>free_for_read</oa></addata></record> |
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| source | ScienceDirect Journals (5 years ago - present); EZB-FREE-00999 freely available EZB journals |
| subjects | Analysis of PDEs Averaging lemma Exact sciences and technology Force term Fourier analysis Fourier series General mathematics General, history and biography Hardy space Kinetic equation Mathematical analysis Mathematics Non-degeneracy conditions Sciences and techniques of general use Stationary phase |
| title | Averaging lemmas with a force term in the transport equation |
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