Title: Dirichlet-to-Neumann or Poincaré-Steklov operator on fractals described by d -sets,
Abstract: In the framework of the Laplacian transport, described by a Robin boundary
value problem in an exterior domain in $\mathbb{R}^n$, we generalize the
definition of the Poincaré-Steklov operator to $d$-set boundaries, $n-2<
d<n$, and give its spectral properties to compare to the spectra of the
interior domain and also of a truncated domain, considered as an approximation
of the exterior case. The well-posedness of the Robin boundary value problems
for the truncated and exterior domains is given in the general framework of
$n$-sets. The results are obtained thanks to a generalization of the continuity
and compactness properties of the trace and extension operators in Sobolev,
Lebesgue and Besov spaces, in particular, by a generalization of the classical
Rellich-Kondrachov Theorem of compact embeddings for $n$ and $d$-sets.