Limiting Bourgain–Brezis estimates for systems of linear differential equations: Theme and variations

Van Schaftingen, Jean
(2014) Journal of Fixed Point Theory and Applications — Vol. 15, n° 2, p. 273-297 (2014)

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Abstract
J. Bourgain and H. Brezis have obtained in 2002 some new and surprising estimates for systems of linear differential equations, dealing with the endpoint case L¹ of singular integral estimates and the critical Sobolev space W1,n(Rn). This paper presents an overview of the results, further developments over the last ten years and challenging open problems.
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Van Schaftingen, J. (2014). Limiting Bourgain–Brezis estimates for systems of linear differential equations: Theme and variations. Journal of Fixed Point Theory and Applications, 15(2), 273-297. https://doi.org/10.1007/s11784-014-0177-0 (Original work published 2014)