Geodesic
Well-posedness of Poincare problem in the cylindrical domain for a class of multi-dimensional elliptic equations
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 10 (2014), pp. 17-25 Cet article a éte moissonné depuis la source Math-Net.Ru

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The boundary value problems for second order elliptic equations in domains with edges are well studied. For elliptic equations, boundary-value problems on the plane were shown to be well posed by using methods from the theory of analytic functions of complex variable. When the number of independent variables is greater than two, difficulties of fundamental nature arise. Highly attractive and convenient method of singular integral equations can hardly be applied, because the theory of multidimensional singular integral equations is still incomplete. In this paper with the help of the method suggested by the author, the unique solvability is shown and explicit form of classical solution of Poincare problem in a cylindrical domain for a one class of multidimensional elliptic equations is received.
Keywords: well-posedness, multi-dimensional elliptic equations, function, cylindrical domain, density, operators, systems of functions.
Mots-clés : equation 
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     author = {S. A. Aldashev},
     title = {Well-posedness of {Poincare} problem in the cylindrical domain for a class of multi-dimensional elliptic equations},
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S. A. Aldashev. Well-posedness of Poincare problem in the cylindrical domain for a class of multi-dimensional elliptic equations. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 10 (2014), pp. 17-25. http://geodesic.mathdoc.fr/item/VSGU_2014_10_a1/

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