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

Bakytbek Danebekovich Koshanov, Alexandr Pavlovich Soldatov

2018

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DOI 10.31489/2018m3/24-30

Data confidence 70 medium

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Abstract

On the solvability of the boundary value problems for the elliptic equation of high order on a planeFor the elliptic equation of 2l-th order with of constant (and only) real coefficients we consider boundary value problem of the normal derivatives (kj -1) order, j = 1, . . ., l, where 1 ≤ k1 < . . .< k l ≤ 2l -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 C 2l,µ (D).We found the condition for Fredholm solvability of this problem and computed the index of this problem.