Differentiability of solutions for the non-degenerate p-Laplacian in the Heisenberg group

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Gradient regularity for elliptic equations in the Heisenberg group (2007, background): “The next lemma summarizes and exploits various difference quotient arguments and results scattered in [15] and [40].”
Regularity results for quasilinear elliptic equations in the Heisenberg group (2007, methodology): “From Theorem 5 and estimate (24), or just from the estimates in [8] and Lemma 3 below, we easily infer that (μ(2) + |Xu|2) p−2 4 Xu ∈ HW 1,2 loc (Ω).”
Higher Hölder regularity for mixed local and nonlocal degenerate elliptic equations (2022, methodology): “Finally, we wish to mention [24], where a similar approach using difference quotients has been used to obtain improved regularity for quasilinear subelliptic equations in theHeisenberg group.”