Geodesic
Estimates for $L^1$-vector fields under higher-order differential conditions
Journal of the European Mathematical Society, Tome 10 (2008) no. 4, pp. 867-882 Cet article a éte moissonné depuis la source EMS Press

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We prove that an L1 vector field whose components satisfy some condition on k-th order derivatives induce linear functionals on the Sobolev space W1,n(Rn). Two proofs are provided, relying on the two distinct methods developed by Bourgain and Brezis (J.\ Eur.\ Math.\ Soc.\ (JEMS), to appear) 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.
DOI : 10.4171/jems/133
Classification : 46-XX, 00-XX
Keywords: Critical Sobolev spaces, compensation, Sobolev inequality, Korn–Sobolev inequality Schrödinger equations, L2-critical NLS, pseudo-conformal blow-up 
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     author = {Jean Van Schaftingen},
     title = {Estimates for $L^1$-vector fields under higher-order differential conditions},
     journal = {Journal of the European Mathematical Society},
     pages = {867--882},
     year = {2008},
     volume = {10},
     number = {4},
     doi = {10.4171/jems/133},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/133/}
}
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Jean Van Schaftingen. Estimates for $L^1$-vector fields under higher-order differential conditions. Journal of the European Mathematical Society, Tome 10 (2008) no. 4, pp. 867-882. doi: 10.4171/jems/133

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