Oscillations of BV measures on unbounded nested fractals

被引：2

作者：

Ruiz, Patricia Alonso ^{[1
]}

Baudoin, Fabrice ^{[2
]}

机构：

[1] Texas A&M Univ, Dept Math, Mailstop 3368, College Stn, TX 77843 USA

[2] Univ Connecticut, Dept Math, 341 Mansfield Rd, U1009, Storrs, CT 06269 USA

来源：

JOURNAL OF FRACTAL GEOMETRY | 2022年 / 9卷 / 3-4期

关键词：

Fractals; functions of bounded variation; oscillations; perimeter measure; BV measures; heat semigroup; geometric functionals; BROWNIAN-MOTION;

D O I：

10.4171/JFG/122

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Motivated by recent developments in the theory of bounded variation functions on unbounded nested fractals, this paper studies the exact asymptotics of functionals related to the total variation measure associated with unions of n -cells. The oscillatory behavior observed implies the non-uniqueness of BV measures in this setting.

引用

页码：373 / 396

页数：24

共 23 条

[1]

Alonso-Ruiz P., ANN FAC SCI TOULOUSE

[2] Besov class via heat semigroup on Dirichlet spaces III: BV functions and sub-Gaussian heat kernel estimates [J].

Alonso-Ruiz, Patricia ;

Baudoin, Fabrice ;

Chen, Li ;

Rogers, Luke ;

Shanmugalingam, Nageswari ;

Teplyaev, Alexander .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2021, 60 (05)

[3] Besov class via heat semigroup on Dirichlet spaces II: BV functions and Gaussian heat kernel estimates [J].

Alonso-Ruiz, Patricia ;

Baudoin, Fabrice ;

Chen, Li ;

Rogers, Luke ;

Shanmugalingam, Nageswari ;

Teplyaev, Alexander .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2020, 59 (03)

[4]

[Anonymous], 1998, Diffusion on Fractals, DOI DOI 10.1007/BFB0092537

[5]

Barlow MT, 2013, CRM PROC & LECT NOTE, V56, P27

[6]

Caccioppoli R., 1952, ATTI ACCAD NAZ LIN, V12, P3

[7]

DEGIORGI E, 1954, ANN MAT PUR APPL, V36, P191, DOI [10.1007/BF02412838, DOI 10.1007/BF02412838]

[8]

Fukushima M., 1992, IDEAS METHODS MATH A, P151

[9] Asymptotics for Functions Associated with Heat Flow on the Sierpinski Carpet [J].

Hambly, B. M. .

CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 2011, 63 (01) :153-180

[10]

Heinonen J., 2015, New Mathematical Monographs

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