A study on harmonic function on Vicsek fractal

被引：2

作者：

Gopalakrishnan, Harsha ^{[1
]}

Prasad, Srijanani Anurag ^{[1
]}

机构：

[1] Indian Inst Technol Tirupati, Dept Math & Stat, Tirupati, India

来源：

CHAOS SOLITONS & FRACTALS | 2024年 / 181卷

关键词：

Vicsek fractal; Renormalization operator; Harmonic function; Mean value property; EXISTENCE;

D O I：

10.1016/j.chaos.2024.114607

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper focuses on the renormalization operator and harmonic functions on the Vicsek fractal. With the help of the Vicsek fractal, we have proven that the renormalization operator need not be unique for a fixed harmonic function. Also, a harmonic extension algorithm may or may not depend on the renormalization factor. Besides, the mean value property of harmonic functions on the Vicsek fractal, a D4 -symmetric fractal, is also given.

引用

页数：7

共 11 条

[1] HARMONIC CALCULUS ON PCF SELF-SIMILAR SETS [J].

KIGAMI, J .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1993, 335 (02) :721-755

[2]

KIGAMI J, 1989, JAPAN J APPL MATH, V6, P259

[3]

Kigami J., 2001, CAMB TRACT MATH

[4] HOW MANY DIFFUSIONS EXIST ON THE VICSEK SNOWFLAKE [J].

METZ, V .

ACTA APPLICANDAE MATHEMATICAE, 1993, 32 (03) :227-241

[5]

Peirone R, 2007, P ROY SOC EDINB A, V137, P1073, DOI 10.1017/S0308210505001137

[6] A p.c.f. self-similar set with no self-similar energy [J].

Peirone, Roberto .

JOURNAL OF FRACTAL GEOMETRY, 2019, 6 (04) :393-404

[7] Existence of self-similar energies on finitely ramified fractals [J].

Peirone, Roberto .

JOURNAL D ANALYSE MATHEMATIQUE, 2014, 123 :35-94

[8] Mean Value Property of Harmonic Functions on the Tetrahedral Sierpinski Gasket [J].

Qiu, Hua ;

Wu, Yipeng ;

Yao, Kui .

JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 2019, 25 (03) :785-803

[9] Mean Value Properties of Harmonic Functions on Sierpinski Gasket Type Fractals [J].

Qiu, Hua ;

Strichartz, Robert S. .

JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 2013, 19 (05) :943-966

[10]

STRICHARTZ RS, 2006, DIFFERENTIAL EQUATIO

← 1 2 →