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Regularity for quasilinear PDEs in Carnot groups via Riemannian approximation
Journal article   Peer reviewed

Regularity for quasilinear PDEs in Carnot groups via Riemannian approximation

Andras Domokos and Juan J Manfredi
Bruno Pini Mathematical Analysis Seminar, Vol.11(1), pp.119-142
03/28/2020
DOI: https://doi.org/10.6092/issn.2240-2829/10589
Handle:
https://hdl.handle.net/20.500.12741/rep:6494

Abstract

riemannian approximation Analysis carnot groups subelliptic, p-laplacian
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}.
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https://doi.org/10.6092/issn.2240-2829/10589View
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