{"id":{"repo_id":"waikato-masters","oai_identifier":"oai:researchcommons.waikato.ac.nz:10289/11383"},"canonical_url":"https://search.dev.ndltd.org/etd/waikato-masters/oai:researchcommons.waikato.ac.nz:10289/11383","repository":{"repo_id":"waikato-masters","name":"University Waikato","base_url":"https://researchcommons.waikato.ac.nz/server/oai/request"},"display":{"title":"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.","abstract_html":"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.","abstract_has_math":false,"creators":["Wang, Michael Yuchuan"],"institution":"The University of Waikato","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Bridges, Douglas","Schroder, Mark"],"committee_chairs":[],"committee_members":[],"year":1996,"date_issued":"1996","date_published":"1996","updated_at":"2026-07-24T05:57:33Z","subjects":["Partial Differential Equations","Constructive Mathematics"],"languages":[],"rights":["All items in Research Commons are provided for private study and research purposes and are protected by copyright with all rights reserved unless otherwise indicated."],"rights_urls":["https://researchcommons.waikato.ac.nz/bitstreams/dbbcc319-81a1-4103-b0f2-27738320f505/download"],"identifier_entries":[]},"links":{"outbound_url":null,"outbound_label":null,"outbound_source":null},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Bridges, Douglas","Schroder, Mark"]},{"key":"dc:creator","label":"Author","values":["Wang, Michael Yuchuan"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.issued","label":"Date","values":["1996"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["The University of Waikato"]},{"key":"dc:relation.isreferencedby","label":"Dc Relation Isreferencedby","values":["https://hdl.handle.net/10289/11383"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Partial Differential Equations","Constructive Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["https://researchcommons.waikato.ac.nz/bitstreams/dbbcc319-81a1-4103-b0f2-27738320f505/download","All items in Research Commons are provided for private study and research purposes and are protected by copyright with all rights reserved unless otherwise indicated."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://researchcommons.waikato.ac.nz/bitstreams/bb9eb06b-1712-43b7-8783-e0fb343a32c0/download"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["This thesis presents the results produced in the study of weak solutions of the Dirichlet Problem within Errett Bishop's constructive mathematics. 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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). 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