A Trace Theorem For Sobolev Spaces On The Sierpinski Gasket

2019/05/08 by Cao, Shiping, Li, Shuangping, Strichartz, Robert S. +1
#28A80 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1905.03391

Abstract

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 L2 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.

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