L^p regularity for elliptic transmission problems with two spectral parameters

ABSTRACT

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

KEYWORDS:

• Elliptic transmission problems
• UMD spaces
• bounded imaginary powers
• analytic semigroups

2020 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 34K10
• 34K30
• 35J25
• 35J40

Disclosure statement

No potential conflict of interest was reported by the author(s).