Regularity for quasilinear PDEs in Carnot groups via Riemannian approximation

András Domokos, Juan J. Manfredi



We study the interior regularity of weak solutions to subelliptic quasilinear PDEs in Carnot groups of the form

Σi=1m1Xi (Φ(|∇Hu|2)Xiu) = 0.

Here ∇Hu = (X1u,...,Xmiu) is the horizontal gradient, δ > 0 and the exponent p ∈ [2, p*), where p* depends on the step ν and the homogeneous dimension Q of the group, and it is given by

p* = min {2ν ∕ ν-1 , 2Q+8 ∕ Q-2}.


Carnot groups; Riemannian approximation; subelliptic, p-Laplacian

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DOI: 10.6092/issn.2240-2829/10589


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