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Advances in Calculus of Variations

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Volume 11, Issue 2

Issues

A note on transport equation in quasiconformally invariant spaces

Albert Clop
  • Department of Mathematics, Faculty of Sciences, Universitat Autònoma de Barcelona,08193 Bellaterra, Barcelona, Catalonia, Spain
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/ Renjin Jiang
  • School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, 100875, Beijing, P. R. China; and Department of Mathematics, Faculty of Sciences, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain
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/ Joan Mateu
  • Department of Mathematics, Faculty of Sciences, Universitat Autònoma de Barcelona,08193 Bellaterra, Barcelona, Catalonia, Spain
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/ Joan Orobitg
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  • Department of Mathematics, Faculty of Sciences, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain
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Published Online: 2016-11-30 | DOI: https://doi.org/10.1515/acv-2016-0003

Abstract

In this note, we study the well-posedness of the Cauchy problem for the transport equation in the BMO space and certain Triebel–Lizorkin spaces.

Keywords: Transport equation; BMO; vector fields; quasiconformal mapping

MSC 2010: 35F05; 35F10

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About the article


Received: 2016-02-02

Accepted: 2016-11-13

Published Online: 2016-11-30

Published in Print: 2018-04-01


Funding Source: Generalitat de Catalunya

Award identifier / Grant number: 2014SGR75

Funding Source: National Natural Science Foundation of China

Award identifier / Grant number: 11301029

Funding Source: Ministerio de Economía y Competitividad

Award identifier / Grant number: MTM2016-75390-P

Albert Clop, Joan Mateu and Joan Orobitg were partially supported by Generalitat de Catalunya (2014SGR75) and Ministerio de Economía y Competitividad (MTM2016-75390-P). Renjin Jiang was partially supported by National Natural Science Foundation of China (NSFC 11301029). All authors were partially supported by Marie Curie Initial Training Network MAnET (FP7-607647).


Citation Information: Advances in Calculus of Variations, Volume 11, Issue 2, Pages 193–202, ISSN (Online) 1864-8266, ISSN (Print) 1864-8258, DOI: https://doi.org/10.1515/acv-2016-0003.

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