Nonconstant Harmonic Functions on the Level 3 Sierpinski Gasket

2014 ◽  
Vol 30 (4) ◽  
pp. 417-424
Author(s):  
D. L. Tang and R. Hu
Keyword(s):  
Harmonic Functions ◽  
Sierpinski Gasket ◽  
Sierpiński Gasket ◽  
Level 3

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

MEAN VALUE PROPERTY OF HARMONIC FUNCTION ON THE HIGHER-DIMENSIONAL SIERPINSKI GASKET

Fractals ◽  
2020 ◽  
Vol 28 (05) ◽  
pp. 2050077
Author(s):  
YIPENG WU ◽  
ZHILONG CHEN ◽  
XIA ZHANG ◽  
XUDONG ZHAO
Keyword(s):  
Harmonic Function ◽  
Harmonic Functions ◽  
Sierpinski Gasket ◽  
Mean Value ◽  
Sierpiński Gasket ◽  
Mean Value Property ◽  
Average Value ◽  
Higher Dimensional ◽  
The Mean

Harmonic functions possess the mean value property, that is, the value of the function at any point is equal to the average value of the function in a domain that contain this point. It is a very attractive problem to look for analogous results in the fractal context. In this paper, we establish a similar results of the mean value property for the harmonic functions on the higher-dimensional Sierpinski gasket.

scholarly journals Absolutely Minimizing Lipschitz Extensions and infinity harmonic functions on the Sierpinski gasket

2017 ◽  
Vol 163 ◽  
pp. 71-85 ◽  
Author(s):  
Fabio Camilli ◽  
Raffaela Capitanelli ◽  
Maria Agostina Vivaldi
Keyword(s):  
Harmonic Functions ◽  
Sierpinski Gasket ◽  
Sierpiński Gasket ◽  
Lipschitz Extensions

scholarly journals Energy measures of harmonic functions on the Sierpinski gasket

2014 ◽  
Vol 63 (3) ◽  
pp. 831-868 ◽  
Author(s):  
Ching wei Ho ◽  
Renee Bell ◽  
Robert S. Strichartz
Keyword(s):  
Harmonic Functions ◽  
Sierpinski Gasket ◽  
Sierpiński Gasket

DIRICHLET PROBLEM OF POISSON EQUATIONS AND VARIATIONAL PRINCIPLE ON A TYPE OF FRACTAL SETS

Fractals ◽  
2020 ◽  
Vol 28 (05) ◽  
pp. 2050090
Author(s):  
YIPENG WU ◽  
KUI YAO ◽  
LEI MU ◽  
ZHILONG CHEN
Keyword(s):  
Dirichlet Problem ◽  
Variational Principle ◽  
Green’S Function ◽  
Green's Function ◽  
Sierpinski Gasket ◽  
Sierpiński Gasket ◽  
Fractal Sets ◽  
Poisson Equations ◽  
Level 3

This paper studied the level-3 Sierpinski gasket. We solved Dirichlet problem of Poisson equations and proved variational principle on the level-3 Sierpinski gasket by expressing Green’s function explicitly.

Sign in / Sign up

Export Citation Format

Share Document