Maximal regularity properties of Agranovich-Vishik type abstract elliptic operators in the half-plane

Abstract

In this work, Agranovich-Vishik type abstract elliptic operators in the half-plane are studied. We derive maximal regularity properties of these operators in UMD-valued Sobolev spaces. Our main aim is to prove existence and uniqueness theorems for the solution of abstract elliptic equation with regular boundary conditions on these function spaces. First, by applying the Fourier multiplier, we prove the separability properties of this differential operator in R-n. By using the embedding theorem and the trace theorem, we obtain the main result.