Bridges, Douglas; Wang, Yuchuan Constructive weak solutions of the Dirichlet problem. (English) Zbl 0929.31004 J. Lond. Math. Soc., II. Ser. 57, No. 3, 655-667 (1998). 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 \(\Omega\). Reviewer: Stephen Gardiner (Dublin) Cited in 2 Documents MSC: 31B20 Boundary value and inverse problems for harmonic functions in higher dimensions 03F60 Constructive and recursive analysis Keywords:weak solution; Bishop’s constructive mathematics; Dirichlet problem PDFBibTeX XMLCite \textit{D. Bridges} and \textit{Y. Wang}, J. Lond. Math. Soc., II. Ser. 57, No. 3, 655--667 (1998; Zbl 0929.31004) Full Text: DOI