We present a survey of recent results from the functional analysis that allow 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 to domains with boundaries carrying measures that are not necessarily Ahlfors $d$-regular. We prove generalizations of the Rellich-Kondrachov theorem and the compactness of the trace operator and obtain uniqueness and existence results for weak solutions to Poisson boundary value problems with Robin boundary conditions. We observe the usual properties of the associated spectral problem.