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

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Embeddings for A-weakly differentiable functions on domains (2017, background): “This and substantial contributions in [9, 10, 11, 5, 7, 6, 8, 52, 53, 54, 55] lead to the remarkable characterization by Van Schaftingen [56] of all k–homogeneous linear differential operators A such that ‖Du‖L1∗ (Rn) 6 c‖Au‖L1(Rn) (1.”
Limiting Sobolev inequalities for vector fields and canceling linear differential operators (2011, unknown): “Proposition 2.4 (Van Schaftingen, 2008 [44, theorem 4]).”
Limiting Bourgain–Brezis estimates for systems of linear differential equations: Theme and variations (2014, methodology): “The proof has also been adapted by constructing φn more carefully than by a mere extension to estimates under higher-order conditions [107], [105], [27, Lemma 2.”