ON THE WELL-POSEDNESS OF ELLIPTIC EQUATIONS WITH NONLOCAL BOUNDARY CONDITIONS

In this paper, we study the abstract nonlo cal boundary value problem for the elliptic equation in an arbitrary Banach space with the positive operator. We establish the well posedness of this nonlo cal boundary value problem across several Banach spaces. Additionally, we derive new Schauder types of coercive stability estimates for the solutions of several nonlo cal boundary value problems involving elliptic equations.