A Dirichlet Form on the Sierpinski Gasket, Related Function Spaces, and Traces

2004 ◽  
pp. 235-244 ◽  
Author(s):  
Alf Jonsson
Keyword(s):  
Dirichlet Form ◽  
Sierpinski Gasket ◽  
Function Spaces ◽  
Sierpiński Gasket ◽  
Related Function

scholarly journals HARMONIC GRADIENTS ON HIGHER-DIMENSIONAL SIERPIŃSKI GASKETS

Fractals ◽  
2020 ◽  
Vol 28 (06) ◽  
pp. 2050108
Author(s):  
LUKE BROWN ◽  
GIOVANNI FERRER ◽  
GAMAL MOGRABY ◽  
LUKE G. ROGERS ◽  
KARUNA SANGAM
Keyword(s):  
Dirichlet Form ◽  
Sierpinski Gasket ◽  
Sharp Contrast ◽  
Standard Measure ◽  
Sierpiński Gasket ◽  
Higher Dimensional ◽  
Sierpinski Gaskets ◽  
Funct Anal

We consider criteria for the differentiability of functions with continuous Laplacian on the Sierpiński Gasket and its higher-dimensional variants [Formula: see text], [Formula: see text], proving results that generalize those of Teplyaev [Gradients on fractals, J. Funct. Anal. 174(1) (2000) 128–154]. When [Formula: see text] is equipped with the standard Dirichlet form and measure [Formula: see text] we show there is a full [Formula: see text]-measure set on which continuity of the Laplacian implies existence of the gradient [Formula: see text], and that this set is not all of [Formula: see text]. We also show there is a class of non-uniform measures on the usual Sierpiński Gasket with the property that continuity of the Laplacian implies the gradient exists and is continuous everywhere in sharp contrast to the case with the standard measure.

scholarly journals Dimer Coverings on the Sierpinski Gasket

2008 ◽  
Vol 131 (4) ◽  
pp. 631-650 ◽  
Author(s):  
Shu-Chiuan Chang ◽  
Lung-Chi Chen
Keyword(s):  
Sierpinski Gasket ◽  
Sierpiński Gasket

scholarly journals Metric approximations of spectral triples on the Sierpiński gasket and other fractal curves

2021 ◽  
Vol 385 ◽  
pp. 107771
Author(s):  
Therese-Marie Landry ◽  
Michel L. Lapidus ◽  
Frédéric Latrémolière
Keyword(s):  
Sierpinski Gasket ◽  
Sierpiński Gasket ◽  
Spectral Triples

scholarly journals Level sets of harmonic functions on the Sierpiński gasket

2002 ◽  
Vol 40 (2) ◽  
pp. 335-362 ◽  
Author(s):  
Anders Öberg ◽  
Robert S. Strichartz ◽  
Andrew Q. Yingst
Keyword(s):  
Level Sets ◽  
Harmonic Functions ◽  
Sierpinski Gasket ◽  
Sierpiński Gasket

Design Sierpinski Gasket Antenna for WLAN Application

2007 ◽  
Author(s):  
C.Z.C. Ghani ◽  
M.H.A. Wahab ◽  
N. Abdullah ◽  
S.A Hamzah ◽  
A. Ubin ◽  
...  
Keyword(s):  
Sierpinski Gasket ◽  
Sierpiński Gasket
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