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Constructive Analysis of Partial Differential Equations
Wang, Michael Yuchuan
Bridges, Douglas
Schroder, Mark
This thesis presents the results produced in the study of weak solutions of the Dirichlet Problem within Errett Bishop's constructive mathematics. It roughly falls into three major parts: a critical analysis of the classical approaches from a constructive point of view (Chapter 2); constructive results on the existence, stability, and maximality of weak solutions (Chapter 5); and related results on the domains discovered during the course of study on the Dirichlet Problem (Chapters 3 and 6). Chapter 1 introduces constructive mathematics, and Chapter 4 is an auxiliary one in which I give two different constructions of a cut-off function.
The University of Waikato
1996
Thesis
en
https://hdl.handle.net/10289/11383
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Partial Differential Equations
Constructive Mathematics