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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"
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.
elliptic equation, boundary value problem, normal derivatives, many connected domain, smooth contour, Fredholm property, index formula.
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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
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\paper A boundary value problem for higher order elliptic equations in many connected domain on the plane
\jour Vladikavkaz. Mat. Zh.
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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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