TY - JOUR
AU - Aldashov, S. A.
PY - 2018/12/28
Y2 - 2024/10/05
TI - A criterion for the unique solvability of the spectral Dirichlet problem in a cylindrical domain for a class of multidimensional elliptic equations
JF - Journal of Mathematics, Mechanics and Computer Science
JA - JMMCS
VL - 96
IS - 4
SE - Mathematics
DO -
UR - https://bm.kaznu.kz/index.php/kaznu/article/view/566
SP - 23-30
AB - <p>Correctness of boundary problems in the plane for elliptic equations is well analyzed by analitic<br>function theory of complex variable. There appear principal difficulties in similar problems when<br>the number of independent variables is more than two. An attractive and suitable method of<br>singular integral equations is less strong because of lock of any complete theory of multidimensional<br>singular integral equations. In the cylindrical domain of Euclidean space, for a single class of<br>multidimensional elliptic equations, the spectral Dirichlet problem with homogeneous boundary<br>conditions is considered. The solution is sought in the form of an expansion in multidimensional<br>spherical functions. The existence and uniqueness theorems of the solution are proved. Conditions<br>for unique solvability of the problem are obtained, which essentially depend on the height of the<br>cylinder.</p>
ER -