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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.
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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