Open AccessOn the Solvability of the Generalized Neumann Problem for a Higher-Order Elliptic Equation in an Infinite Domain
Author(s) -
B. D. Koshanov,
B. D. Koshanov,
A. V. Soldatov,
A. V. Soldatov
Publication year - 2021
Publication title -
sovremennaâ matematika. fundamentalʹnye napravleniâ
Language(s) - English
Resource type - Journals
eISSN - 2949-0618
pISSN - 2413-3639
DOI - 10.22363/2413-3639-2021-67-3-564-575
Subject(s) - mathematics , bounded function , domain (mathematical analysis) , neumann boundary condition , elliptic curve , dirichlet problem , order (exchange) , mathematical analysis , constant (computer programming) , infinity , pure mathematics , dirichlet distribution , boundary value problem , finance , computer science , programming language , economics
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){(k_j - 1)}th-order normal derivatives where 1≤k1...kl≤2l{1\le k_1 < ... < k_l \le 2l}; for kj=j{k_j = j} it turns into the Dirichlet problem, and for kj=j+1{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 Holder spaces is given.