On the differentiability of very weak solutions with right-hand side data integrable with respect to the distance to the boundary

By J. I. Díaz, J. Rakotoson. 2009

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A Priori Estimates for Fractional Nonlinear Degenerate Diffusion Equations on Bounded Domains (2013, methodology): “In the elliptic case, the above definition of very weak solution, has been first given by Brezis (unpublished note), mentioned and used in [23], see also [13] .”
On grand and small Lebesgue and Sobolev spaces and some applications to PDE's (2018, unknown): “Observe that when θ = 1 we have L( n n−1 (Ω) ⊂ L n n−1 (Ω) , hence Theorem 3 improves the corresponding results appeared in [17, 50, 146].”
Finite and infinite energy solutions of singular elliptic problems: Existence and uniqueness (2016, background): “Co nsider for simplicity a functionf as datum; in [20] the authors prove that, if the lower order term (h(u)f in our case) belongs to L1(Ω, δ), for some0 < α < 1, thenu ∈ W 1,q 0 (Ω), for someq > 1.”