{"id":{"repo_id":"brazil-ufrn","oai_identifier":"oai:repositorio.ufrn.br:123456789/51187"},"canonical_url":"https://search.dev.ndltd.org/etd/brazil-ufrn/oai:repositorio.ufrn.br:123456789/51187","repository":{"repo_id":"brazil-ufrn","name":"Brazil UFRN","base_url":"https://repositorio.ufrn.br/server/oai/request"},"display":{"title":"Sobre a teoria de regularidade elíptica via análise da equação de Helmholtz em RN","abstract":"In this work we present an important regularity result for the Helmholtz Equation in unbounded domains due to C. A. Stuart and, furthermore, we show that this result can also be used to regularize weak solutions of nonlinear elliptic problems in RN. In order to achieve our goals, it will be of vital importance the use of Bessel’s Modified Function Theory, Calderón-Zygmund Theory, the Mountain Pass Theorem and Schauder’s Theorem, as well as basic results of Measure and Integration, Complex Analysis, Functional Analysis and the Theory of Sobolev Spaces.","abstract_html":"In this work we present an important regularity result for the Helmholtz Equation in unbounded domains due to C. A. Stuart and, furthermore, we show that this result can also be used to regularize weak solutions of nonlinear elliptic problems in RN. In order to achieve our goals, it will be of vital importance the use of Bessel’s Modified Function Theory, Calderón-Zygmund Theory, the Mountain Pass Theorem and Schauder’s Theorem, as well as basic results of Measure and Integration, Complex Analysis, Functional Analysis and the Theory of Sobolev Spaces.","abstract_has_math":false,"creators":["Silva, Victor Rafael Santos"],"institution":"Universidade Federal do Rio Grande do Norte","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Souza, Diego Ferraz de"],"committee_chairs":[],"committee_members":[],"year":2022,"date_issued":"2022-12-22","date_published":"2022-12-22","updated_at":"2026-07-24T01:20:51Z","subjects":["Equações diferenciais parciais elípticas","Equação de Helmholtz","Métodos variacionais","Funções modificadas de Bessel","Teorema de Agmon-Douglis-Nirenberg"],"languages":["pt_BR"],"rights":["Acesso Aberto"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://repositorio.ufrn.br/handle/123456789/51187","outbound_label":"Repository record","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Souza, Diego Ferraz de"]},{"key":"dc:creator","label":"Author","values":["Silva, Victor Rafael Santos"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2023-02-03T21:11:40Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2023-02-03T21:11:40Z"]},{"key":"dc:date.issued","label":"Date","values":["2022-12-22"]},{"key":"dc:publisher","label":"Institution","values":["Universidade Federal do Rio Grande do Norte"]},{"key":"dc:type","label":"Dc Type","values":["masterThesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Equações diferenciais parciais elípticas","Equação de Helmholtz","Métodos variacionais","Funções modificadas de Bessel","Teorema de Agmon-Douglis-Nirenberg"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["pt_BR"]},{"key":"dc:rights","label":"Dc Rights","values":["Acesso Aberto"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://repositorio.ufrn.br/handle/123456789/51187"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In this work we present an important regularity result for the Helmholtz Equation in unbounded domains due to C. A. Stuart and, furthermore, we show that this result can also be used to regularize weak solutions of nonlinear elliptic problems in RN. In order to achieve our goals, it will be of vital importance the use of Bessel’s Modified Function Theory, Calderón-Zygmund Theory, the Mountain Pass Theorem and Schauder’s Theorem, as well as basic results of Measure and Integration, Complex Analysis, Functional Analysis and the Theory of Sobolev Spaces."]},{"key":"dc:title","label":"Title","values":["Sobre a teoria de regularidade elíptica via análise da equação de Helmholtz em RN"]}]}],"canonical_facts":{"dc:contributor.advisor":["Souza, Diego Ferraz de"],"dc:creator":["Silva, Victor Rafael Santos"],"dc:date.accessioned":["2023-02-03T21:11:40Z"],"dc:date.available":["2023-02-03T21:11:40Z"],"dc:date.issued":["2022-12-22"],"dc:description.abstract":["In this work we present an important regularity result for the Helmholtz Equation in unbounded domains due to C. A. Stuart and, furthermore, we show that this result can also be used to regularize weak solutions of nonlinear elliptic problems in RN. In order to achieve our goals, it will be of vital importance the use of Bessel’s Modified Function Theory, Calderón-Zygmund Theory, the Mountain Pass Theorem and Schauder’s Theorem, as well as basic results of Measure and Integration, Complex Analysis, Functional Analysis and the Theory of Sobolev Spaces."],"dc:identifier.uri":["https://repositorio.ufrn.br/handle/123456789/51187"],"dc:language":["pt_BR"],"dc:publisher":["Universidade Federal do Rio Grande do Norte"],"dc:rights":["Acesso Aberto"],"dc:subject":["Equações diferenciais parciais elípticas","Equação de Helmholtz","Métodos variacionais","Funções modificadas de Bessel","Teorema de Agmon-Douglis-Nirenberg"],"dc:title":["Sobre a teoria de regularidade elíptica via análise da equação de Helmholtz em RN"],"dc:type":["masterThesis"]},"updated_at":"2026-07-24T01:20:51Z"}