Calculus of Variations and Geometric Measure Theory

V. Chousionis - V. Magnani - J. Tyson

Removable sets for Lipschitz harmonic functions on Carnot groups

created by magnani on 21 Oct 2013
modified on 24 Jul 2015


Published Paper

Inserted: 21 oct 2013
Last Updated: 24 jul 2015

Journal: Calc. Var. Partial Differential Equations
Volume: 53
Number: 3-4
Pages: 755–780
Year: 2015


Let $\mathbb G$ be a Carnot group with homogeneous dimension $Q \geq 3$ and let $\mathcal L$ be a sub-Laplacian on $\mathbb G$. We prove that the critical dimension for removable sets of Lipschitz $\mathcal L$-harmonic functions is $(Q-1)$. Moreover we construct self-similar sets with positive and finite ${\mathcal H}^{Q-1}$ measure which are removable.

Tags: GeMeThNES