{"id":{"repo_id":"houston","oai_identifier":"oai:uh-ir.tdl.org:10657/395"},"canonical_url":"https://search.dev.ndltd.org/etd/houston/oai:uh-ir.tdl.org:10657/395","repository":{"repo_id":"houston","name":"University of Houston","base_url":"https://uh-ir.tdl.org/server/oai/request"},"display":{"title":"EXTERIOR REGULARIZED HARMONIC AND HARMONIC FUNCTIONS","abstract":"This thesis mainly studies harmonic functions on exterior regions, having compact, Lipschitz boundaries, in our new finite energy function space, via the sequence of exterior harmonic Steklov eigenvalues and associated eigenfunctions. The new space is strictly larger than the standard Sobolev-Hilbert H-space, as it only needs square integrability of the gradients of the functions involved. Our results generalize exactly certain well-known results on Laplace's spherical harmonics in classical mathematical physics.","abstract_html":"This thesis mainly studies harmonic functions on exterior regions, having compact, Lipschitz boundaries, in our new finite energy function space, via the sequence of exterior harmonic Steklov eigenvalues and associated eigenfunctions. The new space is strictly larger than the standard Sobolev-Hilbert H-space, as it only needs square integrability of the gradients of the functions involved. Our results generalize exactly certain well-known results on Laplace's spherical harmonics in classical mathematical physics.","abstract_has_math":false,"creators":["Han, Qi 1980-"],"institution":"University of Houston","degree_name":"Doctor of Philosophy","degree_level":"Doctoral","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":[],"advisors":["Auchmuty, Giles"],"committee_chairs":[],"committee_members":["Gorb, Yuliya","Onofrei, Daniel","Zhou, Jianxin"],"year":2012,"date_issued":"2012-08","date_published":"2012-08","updated_at":"2026-07-24T02:32:47Z","subjects":["Harmonic functions","Exterior regions","Finite energy space","Steklov eigenvalue problems"],"languages":["eng"],"rights":["The author of this work is the copyright owner. UH Libraries and the Texas Digital Library have their permission to store and provide access to this work. Further transmission, reproduction, or presentation of this work is prohibited except with permission of the author(s)."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/10657/395","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Auchmuty, Giles"]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Gorb, Yuliya","Onofrei, Daniel","Zhou, Jianxin"]},{"key":"dc:creator","label":"Author","values":["Han, Qi 1980-"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2013-07-16T15:43:58Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2013-07-16T15:43:58Z"]},{"key":"dc:date.issued","label":"Date","values":["2012-08"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Doctoral"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Houston"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Harmonic functions","Exterior regions","Finite energy space","Steklov eigenvalue problems"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["The author of this work is the copyright owner. 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