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Solution of the Dirichlet problem for the Poisson equation in some domains with complicated structure of the boundary. (Russian) Zbl 0731.35029
Soobshch. Prikl. Mat., Akad. Nauk SSSR, Vychisl. Tsentr, Mosk. 1989, 44 p. (1989).
The authors discuss the homogeneous Dirichlet problem for Poisson’s differential equation with constant right hand side when the region is either a circle intersected with an arbitrary angle or polygonal domain with an angle rounded by an arc of circle. The solutions are constructed by using the method of conformal mappings. As an application, problems of torsion of prismatic bars with sections of above-mentioned type are solved analytically. In the case of some particular problems the suggested methods are realized numerically.
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation