New Results on Elliptic Equations with Nonlocal Boundary Coefficient-Operator Conditions in UMD Spaces: Noncommutative Cases

Abstract

This paper is devoted to the abstract study of operational second-order differential equations of elliptic type with nonregular coefficient-operator boundary conditions in a non-commutative framework. The study is performed when the second member f belongs to $$L^{p}(0,1;X)$$, with general $$p\in ]1,+\infty [$$, X being a UMD Banach space. We give some new results by using semigroups and interpolation theory. Existence, uniqueness and optimal regularity of the classical and semi-classical solution are proved. This paper improves naturally the ones studied in the commutative case by Hammou et al. (Mediterr J Math, 1669–1683, 2015).