On the Solvability of the Generalized Neumann Problem for a Higher-Order Elliptic Equation in an Infinite Domain

被引：0

作者：

Koshanov B.D. ^{[1
]}

Soldatov A.P. ^{[2
]}

机构：

[1] Institute of Mathematics and Mathematical Modeling, Almaty

[2] Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, Moscow

来源：

Journal of Mathematical Sciences | 2024年 / 278卷 / 2期

关键词：

2lth-order elliptic equation; Fredholm property; generalized Neumann problem; Hölder space; index; infinite domain;

D O I：

10.1007/s10958-024-06924-5

中图分类号：

学科分类号：

摘要：

We consider the generalized Neumann problem for a 2lth-order elliptic equation with constant real higher-order coefficients in an infinite domain containing the exterior of some circle and bounded by a sufficiently smooth contour. It consists in specifying of the (kj − 1)th-order normal derivatives where 1 ≤ k 1 <.. < kl ≤ 2l; for kj = j it turns into the Dirichlet problem, and for kj = j + 1 into the Neumann problem. Under certain assumptions about the coefficients of the equation at infinity, a necessary and sufficient condition for the Fredholm property of this problem is obtained and a formula for its index in Hölder spaces is given. © 2024, Springer Nature Switzerland AG.

引用

页码：342 / 353

页数：11

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