{"id":{"repo_id":"wfu","oai_identifier":"oai:wakespace.lib.wfu.edu:10339/59325"},"canonical_url":"https://search.dev.ndltd.org/etd/wfu/oai:wakespace.lib.wfu.edu:10339/59325","repository":{"repo_id":"wfu","name":"Wake Forest University","base_url":"https://wakespace.lib.wfu.edu/oai/request"},"display":{"title":"Neumann Solutions to a Two-Phase Elliptic Free Boundary Problem in R^2","abstract":"This thesis concerns the problem of minimizing a particular energy functional over an appropriate class of admissible functions on a bounded, convex domain in two-dimensional Euclidean space. We require admissible functions to satisfy Dirichlet boundary conditions on a portion of the fixed boundary with positive one-dimensional Hausdorff measure and Neumann boundary conditions on the rest of the fixed boundary. In this thesis we consider the behavior of minimizers in a neighborhood of some point on the Neumann fixed boundary. The primary result is that minimizers are Lipschitz continuous up to the Neumann fixed boundary.","abstract_html":"This thesis concerns the problem of minimizing a particular energy functional over an appropriate class of admissible functions on a bounded, convex domain in two-dimensional Euclidean space. We require admissible functions to satisfy Dirichlet boundary conditions on a portion of the fixed boundary with positive one-dimensional Hausdorff measure and Neumann boundary conditions on the rest of the fixed boundary. In this thesis we consider the behavior of minimizers in a neighborhood of some point on the Neumann fixed boundary. The primary result is that minimizers are Lipschitz continuous up to the Neumann fixed boundary.","abstract_has_math":false,"creators":["Moon, Gary Alan"],"institution":"Wake Forest University","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2016,"date_issued":"2016","date_published":"2016","updated_at":"2026-07-27T22:02:05Z","subjects":["Analysis"],"languages":["en"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/10339/59325","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Moon, Gary Alan"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2016-05-21T08:35:53Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2017-05-20T08:30:09Z"]},{"key":"dc:date.issued","label":"Date","values":["2016"]},{"key":"dc:publisher","label":"Institution","values":["Wake Forest University"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Analysis"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10339/59325"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["This thesis concerns the problem of minimizing a particular energy functional over an appropriate class of admissible functions on a bounded, convex domain in two-dimensional Euclidean space. We require admissible functions to satisfy Dirichlet boundary conditions on a portion of the fixed boundary with positive one-dimensional Hausdorff measure and Neumann boundary conditions on the rest of the fixed boundary. In this thesis we consider the behavior of minimizers in a neighborhood of some point on the Neumann fixed boundary. The primary result is that minimizers are Lipschitz continuous up to the Neumann fixed boundary."]},{"key":"dc:title","label":"Title","values":["Neumann Solutions to a Two-Phase Elliptic Free Boundary Problem in R^2"]}]}],"canonical_facts":{"dc:creator":["Moon, Gary Alan"],"dc:date.accessioned":["2016-05-21T08:35:53Z"],"dc:date.available":["2017-05-20T08:30:09Z"],"dc:date.issued":["2016"],"dc:description.abstract":["This thesis concerns the problem of minimizing a particular energy functional over an appropriate class of admissible functions on a bounded, convex domain in two-dimensional Euclidean space. We require admissible functions to satisfy Dirichlet boundary conditions on a portion of the fixed boundary with positive one-dimensional Hausdorff measure and Neumann boundary conditions on the rest of the fixed boundary. In this thesis we consider the behavior of minimizers in a neighborhood of some point on the Neumann fixed boundary. The primary result is that minimizers are Lipschitz continuous up to the Neumann fixed boundary."],"dc:identifier.uri":["http://hdl.handle.net/10339/59325"],"dc:language.iso":["en"],"dc:publisher":["Wake Forest University"],"dc:subject":["Analysis"],"dc:title":["Neumann Solutions to a Two-Phase Elliptic Free Boundary Problem in R^2"],"dc:type":["Thesis"]},"updated_at":"2026-07-27T22:02:05Z"}