Laplaciano de Dirichlet em faixas com cantos

• Autor(a) principal: Silva, Kauane de Araujo
• Data de Publicação: 2022
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da UFSCAR
• Texto Completo: https://repositorio.ufscar.br/handle/ufscar/15708
• topic: Laplaciano de Dirichlet; Faixas com cantos; Espectro; Formas quadráticas; Espectro essencial; Espectro discreto; Dirichlet Laplacian; Strips with corners; Spectrum; Quadratic forms; Essential spectrum; Discrete spectrum; CIENCIAS EXATAS E DA TERRA::MATEMATICA::ANALISE::ANALISE FUNCIONAL

Let $\Omega_\theta$ be an unbounded V-shaped set of the plane $\mathbb{R}^2$ , that is, a strip with a corner, and consider $ - \Delta^{D}_{\Omega_\theta}$ the Dirichlet Laplacian in $ \Omega_\theta$. In this work, we will study the spectral problem of $ - \Delta^{D}_{\Omega_\theta}$ and show how its spectral properties essentially depend on a single parameter, the opening angle of the region. We will characterize the essential spectrum of the operator and, in addition, to ensure the existence of its discrete spectrum, we will also find some properties for such a set. In particular, about its finiteness and how the opening of the strip influences this quantity.