Noncoercive Boundary Value Problems for Elliptic Partial Differential and Differential-Operator Equations

Abstract

In this paper we find conditions guarantee that irregular boundary value problems for elliptic differential-operator equations of the second order in an interval are fredholm. We apply this result to find some algebraic conditions guarantee that irregular boundary value problems for elliptic partial differential equations of the second order in cylindrical domains are fredholm. Apparently this is the first paper where the regularity of an elliptic boundary value problem is not satisfied on a manifold of the dimension equal to dimension of the boundary. Nevertheless the problem is fredholm and the resolvent is compact. It is interesting to note that the considered boundary value problems for elliptic equations in a cylinder being with separating variables are noncoercive.