Geodesic
Correctness of the local boundary value problem in a cylindrical domain for one class of multidimensional elliptic equations
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 1-2 (2016), pp. 7-17

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Correctness of boundary value problems in a plane for elliptical equations has been studied properly using the method of the theory of analytic functions. At investigation of analogous problems, when the number of independent variables is more than two, there arise principle difficulties. Quite good and convenient method of singular integral equations has to be abandoned because there is no complete theory of multidimensional singular integral equations. Boundary value problems for second-order elliptical equations in domains with edges have been studied properly earlier. Explicit classical solutions to Dirichlet and Poincare problems in cylindrical domains for one class of multidimensional elliptical equations can be found in the author’s works. In this article, the author proved that the local boundary value problem, which is the generalization of Dirichet and Poincare problem, has only solution. Besides, the criterion of uniqueness of regular solution is obtained.
Keywords: multidimensional elliptical equation, local boundary value problem, cylindrical domain, criterion of uniqueness, Bessel function. 
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     author = {S. A. Aldashev},
     title = {Correctness of the local boundary value problem in a cylindrical domain for one class of multidimensional elliptic equations},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {7--17},
     publisher = {mathdoc},
     number = {1-2},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2016_1-2_a0/}
}
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S. A. Aldashev. Correctness of the local boundary value problem in a cylindrical domain for one class of multidimensional elliptic equations. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 1-2 (2016), pp. 7-17. http://geodesic.mathdoc.fr/item/VSGU_2016_1-2_a0/