Boundary value problem with normal derivatives for a higher-order elliptic equation on the plane

Abstract

For an elliptic operator of order 2l with constant (and only leading) real coefficients, we consider a boundary value problem in which the normal derivatives of order (k_j −1), j = 1,..., l, where 1 ≤ k₁ < ··· < k_l, are specified. It becomes the Dirichlet problem for kj = j and the Neumann problem for k_j = j + 1. We obtain a sufficient condition for the Fredholm property of which problem and derive an index formula.