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Constructive weak solutions of the Dirichlet problem. (English) Zbl 0929.31004

This paper is concerned with constructing a weak solution for the Dirichlet problem within the framework of Bishop’s constructive mathematics. The construction is achieved for a certain type of totally bounded open set \(\Omega\) in \(\mathbb{R}^N\). The authors also discuss the continuous dependence of this solution on the boundary function and on \(\Omega\).

MSC:

31B20 Boundary value and inverse problems for harmonic functions in higher dimensions
03F60 Constructive and recursive analysis
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