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

Abstract

For the elliptic equation of 2l-th order with of constant (and only) real coefficients we consider boundary value problem of the normal derivatives ( k_j -1) order, j = 1,...,l, where 1 ≤ k₁ <... < k_l ≤ 2l-1. When k_j = j it moves into the Dirichlet problem, and when k_j = j+1 it moves into the Neumann problem. In SHAPE \* MERGEFORMAT this paper, the study is carried out in space C ^2l,µ ( D ). We found the condition for Fredholm solvability of this problem and computed the index of this problem.