Holmgren’s Problem for the Laplace Equation in the Hyperoctant of a Multidimensional Ball
Tuhtasin Ergashev‘‘Tashkent Institute of Irrigation and Agricultural Mechanization Engineers’’, National Research University, 100000, Tashkent, UzbekistanM. O. AbbasovaNamangan State University, 160136, Namangan, Uzbekistan
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The present work is devoted to the studying of a boundary value problems with the Neumann conditions on the lateral faces of the ball’s hyperoctant and with the Dirichlet condition on the sphere’s hyperoctant for multidimensional Laplace equation. The main result is a proof of the unique solvability of the problems considered. An energy integral method and Green’s function method were used as the main tools in the proof of the main result. All solutions are found in an explicit forms, which contain fundamental (singular) solution of Laplace equation.
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