New estimates for elliptic equations and Hodge type systems

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Embeddings for A-weakly differentiable functions on domains (2017, background): “25], building on their fundamental work on critical case estimates in [2, 3, 4, 5].”
Limiting Bourgain–Brezis estimates for systems of linear differential equations: Theme and variations (2014, methodology): “First, Bourgain and Brezis have observed that the construction of the solution u in Theorem 1.1—and a fortiori in the stronger theorem (Theorem 1.2)—cannot be linear [14, Proposition 2].”
Gradient theory for plasticity via homogenization of discrete dislocations (2008, background): “3] (see also [25] and [3]) we have that if f ∈ L(1)(Ω; R(2)) is a vector field satisfying div f ∈ H(Ω), then f also belong to H(Ω) and the following estimate also holds ‖f‖H−1(Ω) ≤ c ( ‖div f‖H−2(Ω) + ‖f‖L1(Ω) )”