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Trace Results on Domains with Self-Similar Fractal Boundaries Yves Achdou
 

Summary: Trace Results on Domains with Self-Similar 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 self-similar fractal boundary
. The fractal boundary
is supplied with a
probability measure µ called the self-similar measure. Emphasis is put on the case when the
domain is not a - domain and the fractal is not post-critically 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

  

Source: Achdou, Yves - Laboratoire Jacques-Louis Lions, Université Pierre-et-Marie-Curie, Paris 6

 

Collections: Mathematics