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 Vladikavkaz. Mat. Zh., 2017, Volume 19, Number 3, Pages 51–58 (Mi vmj624)

A boundary value problem for higher order elliptic equations in many connected domain on the plane

A. P. Soldatov

National Research University "Belgorod State University"

Abstract: For the elliptic equation of $2l$th order with constant (and leading) coefficients boundary value a problem with normal derivatives of the $(k_j-1)-$order, $j=1,\ldots,l$ considered. Here $1\le k_1 <\ldots< k_l\le 2l$. When $k_j=j$ it moves to the Dirichlet problem, and when $k_j = j + 1$ it corresponds to the Neumann problem. The sufficient condition of the Fredholm problem and index formula are given.

Key words: elliptic equation, boundary value problem, normal derivatives, many connected domain, smooth contour, Fredholm property, index formula.

 Funding Agency Grant Number Ministry of Education and Science of the Russian Federation 1.7311.2017/Á×

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Citation: A. P. Soldatov, “A boundary value problem for higher order elliptic equations in many connected domain on the plane”, Vladikavkaz. Mat. Zh., 19:3 (2017), 51–58

Citation in format AMSBIB
\Bibitem{Sol17} \by A.~P.~Soldatov \paper A boundary value problem for higher order elliptic equations in many connected domain on the plane \jour Vladikavkaz. Mat. Zh. \yr 2017 \vol 19 \issue 3 \pages 51--58 \mathnet{http://mi.mathnet.ru/vmj624} 

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This publication is cited in the following articles:
1. A. A. Andreyev, V. P. Padchenko, E. A. Kozlova, “To the 70th anniversary of professor Alexander Pavlovich Soldatov”, Vestn. Samar. Gos. Tekhnicheskogo Univ.-Ser. Fiz.-Mat. Nauka, 22:1 (2018), 15–22
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