Laplaciano de Dirichlet em faixas com cantos - Silva, Kauane de Araujo (Universidade Federal de São Carlos, 2022)
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.
Dirichlet Laplacian in strips with corners
Keywords: 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