Geodesic
On the solvability of the generalized Neumann problem for a higher-order elliptic equation in an infinite domain
Contemporary Mathematics. Fundamental Directions, Dedicated to 70th anniversary of the President of the RUDN University V. M. Filippov, Tome 67 (2021) no. 3, pp. 564-575

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We consider the generalized Neumann problem for a $2l$th-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 \le k_1 \ldots $ 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. 
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     author = {B. D. Koshanov and A. P. Soldatov},
     title = {On the solvability of the generalized {Neumann} problem for a higher-order elliptic equation in an infinite domain},
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     pages = {564--575},
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     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2021_67_3_a10/}
}
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B. D. Koshanov; A. P. Soldatov. On the solvability of the generalized Neumann problem for a higher-order elliptic equation in an infinite domain. Contemporary Mathematics. Fundamental Directions, Dedicated to 70th anniversary of the President of the RUDN University V. M. Filippov, Tome 67 (2021) no. 3, pp. 564-575. http://geodesic.mathdoc.fr/item/CMFD_2021_67_3_a10/