Regularity for quasilinear PDEs in Carnot groups via Riemannian approximation
DOI:
https://doi.org/10.6092/issn.2240-2829/10589Keywords:
Carnot groups, Riemannian approximation, subelliptic, p-LaplacianAbstract
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}.
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