  We provide a short introduction of new and well-known facts relating
non-local operators and irregular domains. Cauchy problems and boundary value
problems are considered in case non-local operators are involved. Such problems
respectively lead to anomalous behavior on the bulk and on the surface of a
given domain. Such a behavior can be considered (in a macroscopic viewpoint) in
order to describe regular motion on irregular domains (in the microscopic
viewpoint).
