Constructive Analysis of Partial Differential Equations

Abstract

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.