In this thesis, we study how the solution of a PDE changes when the data are rearranged. Specifically, we prove comparison theorems on spherical shells, spheres, and hemispheres, showing that under rearrangement of the data, the solution's convex mean increases. We also obtain similar weighted comparison results in balls.
","abstract_html":"<p>In this thesis, we study how the solution of a PDE changes when the data are rearranged. Specifically, we prove comparison theorems on spherical shells, spheres, and hemispheres, showing that under rearrangement of the data, the solution's convex mean increases. We also obtain similar weighted comparison results in balls.</p>","abstract_has_math":false,"creators":["Langford, Jeffrey"],"institution":null,"degree_name":"Doctor of Philosophy (PhD)","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Albert Baernstein II"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2012,"date_issued":"2012-05-24T07:00:00Z","date_published":"2012-05-24T07:00:00Z","updated_at":"2026-07-24T06:12:25Z","subjects":["Mathematics","Comparison Theorems","Neumann Boundary Conditions","Oscillation Estimates","Rearrangements","Symmetrization"],"languages":["English (en)"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier.doi","label":"DOI","values":["https://doi.org/10.7936/K7R20ZGM"],"render_values":[{"text":"https://doi.org/10.7936/K7R20ZGM","href":"https://doi.org/10.7936/K7R20ZGM","code":true}]}]},"links":{"outbound_url":"https://openscholarship.wustl.edu/etd/706","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Albert Baernstein II"]},{"key":"dc:creator","label":"Author","values":["Langford, Jeffrey"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2014-05-24T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy (PhD)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics","Comparison Theorems","Neumann Boundary Conditions","Oscillation Estimates","Rearrangements","Symmetrization"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English (en)"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://openscholarship.wustl.edu/etd/706"]},{"key":"dc:identifier.doi","label":"DOI","values":["https://doi.org/10.7936/K7R20ZGM"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In this thesis, we study how the solution of a PDE changes when the data are rearranged. Specifically, we prove comparison theorems on spherical shells, spheres, and hemispheres, showing that under rearrangement of the data, the solution's convex mean increases. We also obtain similar weighted comparison results in balls.
"]},{"key":"dc:title","label":"Title","values":["Comparison Theorems in Elliptic Partial Differential Equations with Neumann Boundary Conditions"]}]}],"canonical_facts":{"dc:contributor":["Albert Baernstein II"],"dc:creator":["Langford, Jeffrey"],"dc:date.available":["2014-05-24T07:00:00Z"],"dc:description.abstract":["In this thesis, we study how the solution of a PDE changes when the data are rearranged. Specifically, we prove comparison theorems on spherical shells, spheres, and hemispheres, showing that under rearrangement of the data, the solution's convex mean increases. We also obtain similar weighted comparison results in balls.
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