Fractional-power approach for the study of elliptic second-order boundary-value problems with variable-operator coefficients in an unbounded domain

Abstract

In this article, we give new results on the study of elliptic complete abstract second order differential equations with variable operator coefficients under Dirichlet boundary conditions, and set in ℝ₊. In the framework of Holderian spaces and under some compatibility conditions, we prove the main results on the existence, uniqueness and maximal regularity of the classical solution of this kind of problems which have not been studied in variable coefficients case. We use semigroups theory, fractional powers of linear operators, Dunford's functional calculus and interpolation theory. In this work, we consider some differentiability assumptions on the resolvents of square roots of linear operators.