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Яндекс.Метрика

DOI: 10.23671/VNC.2017.3.7130

A Boundary Value Problem for Higher Order Elliptic Equations in Many Connected Domain on the Plane

Soldatov A. P.
Vladikavkaz Mathematical Journal 2017. Vol. 19. Issue 3.
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.
Keywords: elliptic equation, boundary value problem, normal derivatives, many connected domain, smooth contour, Fredholm property, index formula
Language: Russian Download the full text  
For citation: Soldatov A. P. A boundary value problem for higher order elliptic equations †in many connected domain on the plane Vladikavkazskii matematicheskii zhurnal [Vladikavkaz Math. J.], vol. 19, no. 1, pp. 51-58. DOI 10.23671/VNC.2017.3.7130
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