# A Trace Theorem For Sobolev Spaces On The Sierpinski Gasket

## TL;DR

This paper characterizes the trace of Sobolev spaces on the Sierpinski gasket, including the Laplacian's domain, and identifies trace spaces as Besov spaces for low-order Sobolev spaces.

## Contribution

It provides a discrete characterization of Sobolev space traces on fractals, extending classical trace theorems to the Sierpinski gasket.

## Key findings

- Discrete trace characterization for Sobolev spaces on the gasket
- Identification of trace spaces as Besov spaces for low orders
- Includes the L2 domain of the Laplacian as a special case

## 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.