Superharmonic functions are locally renormalized solutions

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Nonlocal Equations with Measure Data (2014, background): “Such definitions are all equivalent in the case the measure μ is nonnegative, as eventually shown in [31].”
A pocket guide to nonlinear differential equations in Musielak–Orlicz spaces (2018, result): “of p-harmonic elliptic problem with merely integrable data, namely −∆pu = f ∈ L1(Ω). (7) 18 It should be stressed from the beginning that the mentioned distinct notions of solutions can coincide. See [127] for an elliptic result and [82] for the equivalence between entropy and renormalized solutions”
The Wolff gradient bound for degenerate parabolic equations (2014, background): “Also SOLAs are not known to be unique except in special cases (see the discussion in [2, 4, 6, 18, 38]).”
Nonlinear Measure Data Problems (2011, methodology): “As a matter of fact, also when not considering SOLA, existence theorems for measure data problems are always found via approximation methods involving some regularization; see for instance [73, 22, 54].”