Due to the ever-increasing degree of urbanization, blue and green infrastructures are becoming important tools for achieving stormwater management sustainability in urban areas. Concerning green roofs, although scientists have investigated their behaviors under different climates and building practices, their hydrological performance is still a thought-provoking field of research. An event scale analysis based on thirty-five rainfall–runoff events recorded at a new set of experimental green roofs located in Southern Italy has been performed with the aim of identifying the relative roles of climate, substrate moisture conditions, and building practices on retention properties. The retention coefficient showed a wide range of variability, which could not be captured by neither simple nor multiple linear regression analysis, relating the latter to rainfall characteristics and substrate soil water content. Significant improvements in the prediction of the retention coefficient were obtained by a preliminary identification of groups of rainfall–runoff events, based on substrate soil water content thresholds. Within each group, a primary role is played by rainfall. At the experimental site, building practices, particularly those concerning the drainage layer properties, appeared to affect the retention properties only for specific event types.

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In this paper we study certain weighted Sobolev spaces defined on an open subset Ω of R^n (not necessarily bounded or regular) when the weight is a function related to the distance from a subset of ∂Ω. As an application, we prove boundedness and compactness results for operators in such weighted Sobolev spaces

We deepen the study of some Morrey type spaces, denoted byMp,λ(Ω), defined on an unbounded open subsetΩofℝn. In particular, we construct decompositions for functions belonging to two different subspaces ofMp,λ(Ω), which allow us to prove a compactness result for an operator in Sobolev spaces. We also introduce a weighted Morrey type space, settled between the above-mentioned subspaces.

We give an overview on some results concerning the unique solvability of the Dirichlet problem in 2, , > 1, for second-order linear elliptic partial differential equations in nondivergence form and with singular data in weighted Sobolev spaces. We also extend such results to the planar case.