Intrinsic regular graphs in Heisenberg groups vs. weak solutions of non-linear first-order PDEs

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Regularity of non-characteristic minimal graphs in the Heisenberg group $H^1$ (2008, methodology): “In the present paper we require only Lipschitz continuity of u and prove higher order intrinsic differentiability than either [3], and [10].”
Smoothness of Lipschitz minimal intrinsic graphs in Heisenberg groups , n > 1 (2010, result): “A comparison with other regularity results for the case n 1⁄4 1 due to Bigolin and Serra-Cassano [3] is discussed in our paper [6].”
Examples of area-minimizing surfaces in the subriemannian Heisenberg group H^1 with low regularity (2008, background): “We would like also to mention the recently distributed notes by Bigolin and Serra Cassano [5], where they obtain regularity properties of an Hregular surface from regularity properties of its horizontal unit normal.”