On the problem of determining the parameter of an elliptic equation in a Banach space

Abstract

The boundary value problem of determining the parameter of an elliptic equation -u ''(t) + Au(t) = f (t) + p (0 <= t <= T), u(0) = phi, u(T) = psi, u(lambda) = xi, 0 < lambda < T, with a positive operator A in an arbitrary Banach space E is studied. The exact estimates are obtained for the solution of this problem in Holder norms. Coercive stability estimates for the solution of boundary value problems for multi-dimensional elliptic equations are established.