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For higher-order partial differential equations in two or three variables, the Dirichlet problemin rectangular domains is studied. Small denominators hampering the convergence of series appear in the process of constructing the solution of the problem by the spectral decomposition method. A uniqueness criterion for the solution is established. In the two-dimensional case, estimates justifying the...
The properties of mappings by the solutions of second-order elliptic partial differential equations in the plane are studied. We obtain conditions on a function, continuous on the unit circle, that are sufficient for the solution of the Dirichlet problem in the open unit disk for the given equation with the given boundary function to be a homeomorphism between the open unit disk and a Jordan simply...
In view of the problems of grouting pressure with multiple boreholes, according to Fourier series technique and correlative property of singular function, and based on natural boundary element method, the pressure boundary integral formula for Darcy flow equation of interior circular region with Dirichlet boundary value problem and the seepage pressure field of exterior vertical shaft with Neumann...
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