Estimates for $L^1$-vector fields under higher-order differential conditions | Zendy

Jean Van Schaftingen | Zendy

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Estimates for $L^1$-vector fields under higher-order differential conditions

Author(s) -

Jean Van Schaftingen

Publication year - 2008

Publication title -

journal of the european mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 3.549

H-Index - 64

eISSN - 1435-9863

pISSN - 1435-9855

DOI - 10.4171/jems/133

Subject(s) - mathematics , order (exchange) , vector field , vector (molecular biology) , differential (mechanical device) , mathematical analysis , pure mathematics , geometry , finance , economics , biochemistry , chemistry , aerospace engineering , engineering , gene , recombinant dna

We prove that an L-1 vector field whose components satisfy some condition on k-th order derivatives induce linear functionals on the Sobolev space W-1,W-n(R-n). Two proofs are provided, relying on the two distinct methods developed by Bourgain and Brezis (J. Eur. Math. Soc., 2007) and by the author (C. R. Math. Acad. Sci. Paris, 2004) to prove the same result for divergence-free vector fields and partial extensions to higher-order conditions

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