Removable sets for Lipschitz harmonic functions on Carnot groups

Vasilis Chousionis, Valentino Magnani, Jeremy T. Tyson

Research output: Contribution to journalArticlepeer-review

Abstract

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

Original languageEnglish (US)
Article number10
Pages (from-to)755-780
Number of pages26
JournalCalculus of Variations and Partial Differential Equations
Volume53
Issue number3-4
DOIs
StatePublished - Jul 22 2015

Keywords

  • 22E30
  • Primary Classification 42B20
  • Secondary Classification 28A75

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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