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  1. We review the existing literature concerning regularity for the gradient of weak solutions of the subelliptic p-Laplacian differential operator in a domain Ω in the Heisenberg group H^n, with 1 ≤ p < ∞, and of its parabolic counterpart. We present some open problems and outline some of the difficulties they present. 
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  2. We prove local Lipschitz regularity for weak solutions to a class of degenerate parabolic PDEs modeled on the parabolic p-Laplacian $\(\partial_t u= \sum_{i=1}^{2n} X_i (|\nabla_0 u|^{p-2} X_i u),\$ in a cylinder $\(\Omega\times\mathbb{R}^+\)$, where $ \(\Omega\)$ is domain in the Heisenberg group $\(\mathbb{H}^n\)$, and $\(2\le p \le 4\)$. The result continues to hold in the more general setting of contact subRiemannian manifolds. 
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  3. We are delighted to share with you our twelfth Journal Club and highlight some of the most interesting papers published recently [...] 
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