New estimates for the Laplacian, the div-curl, and related Hodge systems

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New estimates for elliptic equations and Hodge type systems (2007, background): “This can be proved by the same argument as in [4], [5], or by the argument due to Van Schaftingen [13], [14].”
Estimates for L-1 vector fields under higher-order differential conditions (2008, methodology): “As Bourgain and Brezis explain [4], it is not known whether their method extends to fractional Sobolev spaces.”
Form boundedness of the general second‐order differential Operator (2004, background): “inequalities, might be useful in further applications to mathematical physics, dynamics, analysis of phases, and other nonlinear problems (see, e.g., [BB1], [ BB2 ], [D3], [IM]).”
Embeddings for A-weakly differentiable functions on domains (2017, background): “This and substantial contributions in [8, 9, 10, 4, 6, 5, 7, 48, 49, 50, 51] lead to the remarkable characterization by Van Schaftingen [52] of all k–homogeneous linear differential operators A such that ‖Du‖L1∗ (Rn) 6 c‖Au‖L1(Rn) (1.”