Sobre a teoria de regularidade elíptica via análise da equação de Helmholtz em RN

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.

Grantor dc:publisher

Universidade Federal do Rio Grande do Norte

Year dc:date.issued

2022

Author dc:creator

• Silva, Victor Rafael Santos

Advisor dc:contributor.advisor

• Souza, Diego Ferraz de

• Equações diferenciais parciais elípticas
• Equação de Helmholtz
• Métodos variacionais
• Funções modificadas de Bessel
• Teorema de Agmon-Douglis-Nirenberg

Statement dc:rights

• Acesso Aberto

Language dc:language

pt_BR

Repository record dc:identifier.uri

https://repositorio.ufrn.br/handle/123456789/51187

OAI identifier oai:identifier

oai:repositorio.ufrn.br:123456789/51187