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arXiv · 1905.03391

A Trace Theorem For Sobolev Spaces On The Sierpinski Gasket

Shiping Cao·Shuangping Li·Robert S. Strichartz·Prem Talwai
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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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Shiping Cao, Shuangping Li, Robert S. Strichartz, Prem Talwai. 2019-05-08. A Trace Theorem For Sobolev Spaces On The Sierpinski Gasket. https://arxiv.org/abs/1905.03391

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