L p regularity for elliptic transmission problems with two spectral parameters

We study a family of elliptic transmission problems on heterogeneous unbounded domains posed in UMD spaces. In order to determine the strict solution, this work investigates the effect and relationships between two spectral parameters; the first parameter is in the differential equation, and the second is in the permeability condition on the interface. Necessary and sufficient conditions on the data are established to prove the maximal regularity of the solution by using semigroup theory and the properties of fractional powers of linear operators