  We present a survey of recent results of the functional analysis allowing to
solve PDEs in a large class of domains with irregular boundaries. We extend the
previously introduced concept of admissible domains with a d-set boundary on
the domains with the boundaries on which the measure is not necessarily Ahlfors
regular d-measure. This gives a generalization of Rellich-Kondrachov theorem
and the compactness of the trace operator, allowing to obtain, as for a regular
classical case the unicity/existence of weak solutions of Poisson boundary
valued problem with the Robin boundary condition and to obtain the usual
properties of the associated spectral problem.
