Regularity for quasilinear PDEs in Carnot groups via Riemannian approximation

Abstract

We study the interior regularity of weak solutions to subelliptic quasilinear PDEs in Carnot groups of the formΣi=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 byp* = min {2ν ∕ ν-1 , 2Q+8 ∕ Q-2}.