A TRACE THEOREM FOR SOBOLEV SPACES ON THE SIERPINSKI GASKET

被引：4

作者：

Cao, Shiping ^{[1
]}

Li, Shuangping ^{[2
]}

Strichartz, Robert S. ^{[1
]}

Talwai, Prem ^{[3
]}

机构：

[1] Cornell Univ, Dept Math, White Hall, Ithaca, NY 14853 USA

[2] Princeton Univ, Program Appl & Computat Math, Princeton, NJ 08544 USA

[3] Columbia Business Sch, Decis Risk & Operat, New York, NY 10027 USA

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2020年 / 19卷 / 07期

关键词：

Sierpinski gasket; Sobolev space; trace theorem; Laplacian; BOUNDARY-VALUE-PROBLEMS; BROWNIAN-MOTION; HARMONIC-FUNCTIONS; DIRICHLET FORMS; FRACTALS; LAPLACIAN; DOMAINS;

D O I：

10.3934/cpaa.2020159

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We give a discrete characterization of the trace of a class of Sobolev spaces on the Sierpinski gasket to the bottom line. This includes the L-2 domain of the Laplacian as a special case. In addition, for Sobolev spaces of low orders, including the domain of the Dirichlet form, the trace spaces are Besov spaces on the line.

引用

页码：3901 / 3916

页数：16

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