 
Summary: Trace Results on Domains with SelfSimilar Fractal Boundaries
Yves Achdou
, Nicoletta Tchou
.
February 10, 2008
Abstract
This work deals with trace theorems for a family of ramified bidimensional domains
with a selfsimilar fractal boundary
. The fractal boundary
is supplied with a
probability measure µ called the selfsimilar measure. Emphasis is put on the case when the
domain is not a  domain and the fractal is not postcritically finite, for which classical
results cannot be used. It is proven that the trace of a function in H1
() belongs to Lp
µ
for all real numbers p 1. A counterexample shows that the trace of a function in H1
()
may not belong to BMO(µ) (and therefore may not belong to L
µ ). Finally, it is proven
that the traces of the functions in H1
