Study of an Elliptic Differential Equation: Set in Three Habitats with Skewness Boundary Conditions at the Interfaces in L^q Cases

In this paper, we give some new results on the maximal regularity of an elliptic differential equation set in three habitats with skewness boundary conditions at the interfaces in UMD spaces. This work completes naturally the results obtained in our paper (Labbas et al. in Mediterr J Math 15(3):128, 2018) studied in H older spaces. Our techniques use essentially the semigroup theory and the celebrated Dore-Venni theorem (Math Z 196:124-136, 1987).