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

Koshanov B.D. Soldatov A.P.
January 2024 Springer

Journal of Mathematical Sciences (United States)
2024 #278 Issue 2 342 - 353 pp.

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 (k_j − 1)th-order normal derivatives where 1 ≤ k ₁ <.. < k_l ≤ 2l; for k_j = j it turns into the Dirichlet problem, and for k_j = 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.

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

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Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, Moscow, Russian Federation

Institute of Mathematics and Mathematical Modeling
Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences

10 лет помогаем публиковать статьи Международный издатель

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