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Numerical solutions of the Dirichlet problem via a density theorem. (English) Zbl 0842.65072
A sharp density result for continuous and also for \(L^p\) real-valued functions is the core of this work. This result is in fact a constructive existence theorem for the 2D Dirichlet problem for Laplace’s equation with continuous or \(L^2\) discontinuous boundary data. The restrictions for the considered domains are slightly stronger than that for simply connected ones. They have piecewise continuously differentiable boundary. This means that the domains can have corners except cusps. Computational examples of Dirichlet problems are analyzed.

MSC:
65N38 Boundary element methods for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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