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
收藏
页码：342 / 353
页数：11
相关论文
共 15 条
  • [1] Bitsadze A.V., Some properties of polyharmonic functions, Diff. Uravn., 24, 5, pp. 825-831, (1988)
  • [2] Kondrat'Ev V.A., Oleynik O.A., On periodic solutions of a second-order parabolic equation in outer domains, Vestn. Mosk. Un-Ta. Ser. 1. Mat. Mekh., 4, pp. 38-47, (1985)
  • [3] Koshanov B.D., Kulimbek Z.K., Behavior of solutions of the Poisson equation and the biharmonic equation, Mat. Zh., 16, 1, pp. 118-134, (2016)
  • [4] Koshanov B., Soldatov A.P., Boundary-value problem with normal derivatives for an elliptic equation on a plane, Diff. Uravn., 52, 12, pp. 1666-1681, (2016)
  • [5] Koshanov B.D., Soldatov A.P., About the generalized Dirichlet-Neumann problem for an elliptic equation of high order, AIP Conference Proceedings, 1997, (2018)
  • [6] Malakhova N.A., Soldatov A.P., On a boundary-value problem for a higher-order elliptic equation, Diff. Uravn., 44, 8, pp. 1077-1083, (2008)
  • [7] Matevosyan O.A., On the uniqueness of the solution of the first boundary-value problem of elasticity theory for unbounded domains, Usp. Mat. Nauk, 48, 6, pp. 159-160, (1993)
  • [8] Matevossian O.A., On solutions of the Neumann problem for the biharmonic equation in unbounded domains, Math. Notes, 98, pp. 990-994, (2015)
  • [9] Nazarov S.A., Plamenevskii B.A., Elliptic Problems in Domains with Piecewise Smooth Boundaries, (1991)
  • [10] Palais R., Seminar on the Atiyah-Singer Index Theorem [Russian translation], (1970)
12