We prove that the critical dimension for removable sets of Lipschitz L-harmonic functions is Q-1, where Q is the Hausdorff dimension of the Carnot group, the sub-Laplacian L is defined and Q is not less than 3. Moreover, we construct self-similar sets with positive and finite Hausdorff measure of dimension Q-1, which are removable.
Autori interni: | |
Autori: | Vasilis Chousionis; Valentino Magnani; Jeremy T. Tyson |
Titolo: | Removable sets for Lipschitz harmonic functions on Carnot groups |
Anno del prodotto: | 2015 |
Abstract: | We prove that the critical dimension for removable sets of Lipschitz L-harmonic functions is Q-1, where Q is the Hausdorff dimension of the Carnot group, the sub-Laplacian L is defined and Q is not less than 3. Moreover, we construct self-similar sets with positive and finite Hausdorff measure of dimension Q-1, which are removable. |
Digital Object Identifier (DOI): | 10.1007/s00526-014-0766-1 |
Appare nelle tipologie: | 1.1 Articolo in rivista |
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