REGULAR BOUNDARY VALUE PROBLEMS FOR ELLIPTIC DIFFERENTIAL-OPERATOR EQUATIONS OF THE FOURTH ORDER IN UMD BANACH SPACES

Abstract

We study Fredholmness of nonlocal boundary value problems for fourth order elliptic differential-operator equations in UMD Banach spaces. The main condition is given in terms of R-boundedness of some families of bounded operators generated by inverse of the characteristic operator pencil of the equation. Then we prove an isomorphism of the problem on the semi-axis, for some special boundary conditions, in appropriate L_p spaces. This implies maximal L_p-regularity for the problem. We also present some relevant application of obtained abstract results to boundary value problems for fourth order elliptic and quasi-elliptic partial differential equations.