Tesis
Laplaciano de Dirichlet em faixas com cantos
Fecha
2022-02-24Registro en:
Autor
Silva, Kauane de Araujo
Institución
Resumen
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.