A remark on an elliptic equation in an unbounded domain

Abstract

We give in this work some remarks on the resolution of an elliptic equation with homogeneous Dirichlet boundary conditions posed on the unbounded domain Σ =(0,+∞ )×(0,1). Our aim is to use the famous Dore-Venni theorem, in UMD Banach spaces, to prove the existence, uniqueness and maximal regularity of the strict solution.