On the solvability of the boundary value problems for the elliptic quation of high order on a plane

Abstract

For the elliptic equation of 21—th order with of constant (and only) real coefficients we consider boundary value problem of the normal derivatives (kj — 1) order, j = 1,... ,1, where 1 < k1 < ... < ki < 21 — 1. When kj = j it moves into the Dirichlet problem, and when kj = j + 1 it moves into the Neumann problem. In this paper, the study is carried out in space C2l,M(D). We found the condition for Fredholm solvability of this problem and computed the index of this problem.