Laplaciano de Dirichlet em faixas com cantos - Silva, Kauane de Araujo (2022)
Let $Ω_θ$ be an unbounded V-shaped set of the plane $\mathbb{R}^2$ , that is, a strip with a corner, and consider $ - Δ^{D}_{Ω_θ}$ the Dirichlet Laplacian in $ Ω_θ$. In this work, we will study the spectral problem of $ - Δ^{D}_{Ω_θ}$ 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.