Abstract
We introduce two fractals, in Euclidean spaces of dimension two and three, respectively, such that the 2-conductive homogeneity holds but there is some " 2 .0; 1/ so that the p-conductive homogeneity fails for every p 2 .1; 1 C "/. In addition, these two fractals have Ahlfors regular conformal dimension within the interval .1; 2/ and .2; 3/, respectively.
Original language | English |
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Pages (from-to) | 93-104 |
Number of pages | 12 |
Journal | Journal of Fractal Geometry |
Volume | 12 |
Issue number | 1-2 |
DOIs | |
Publication status | Published - 2025 |
Externally published | Yes |
Keywords
- conductance
- Dirichlet form
- energy measure
- extension operator
- harmonic function
- Mosco convergence
- Sierpiński carpets
- weak convergence