In the framework of the Laplacian transport, described by a Robin boundary value problem in an exterior domain in 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.
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