USING PEANO CURVES TO CONSTRUCT LAPLACIANS ON FRACTALS

DOI10.1142/S0218348X15500486zbMath1342.28020arXiv1402.2106OpenAlexW3100743161MaRDI QIDQ5739842

Denali Molitor, Nadia Ott, Robert S. Strichartz

Publication date: 5 July 2016

Published in: Fractals (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1402.2106

zbMATH Keywords

Laplacianself-similar fractalsPeano curvemagic carpetpentagasketoctagasket

Mathematics Subject Classification ID

Fractals (28A80)

Related Items (9)

Resistance scaling on \(4N\)-carpets ⋮ Simple fractal calculus from fractal arithmetic ⋮ Hodge-de Rham Theory of K-Forms on Carpet Type Fractals ⋮ Geometry and Laplacian on discrete magic carpets ⋮ MEAN VALUE PROPERTY OF HARMONIC FUNCTION ON THE HIGHER-DIMENSIONAL SIERPINSKI GASKET ⋮ DIRICHLET PROBLEM OF POISSON EQUATIONS AND VARIATIONAL PRINCIPLE ON A TYPE OF FRACTAL SETS ⋮ Dual graphs and modified Barlow-Bass resistance estimates for repeated barycentric subdivisions ⋮ SPECTRUM OF THE LAPLACIAN ON THE VICSEK SET “WITH NO LOOSE ENDS” ⋮ HAUSDORFF DIMENSION OF GENERALIZED FIBONACCI WORD FRACTALS

Cites Work

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• Laplacians on fractals with spectral gaps have nicer Fourier series
• Laplacians on Julia Sets III: Cubic Julia Sets and Formal Matings

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