Espectro do Laplaciano de Dirichlet-Neumann em faixas estreitas - Bello, Diana Carolina Suarez (Universidade Federal de São Carlos, 2020)
Let $\Omega_\varepsilon$ be a thin strip in $\mathbb{R}^2$ and $-\Delta_{DN}^{\Omega_\varepsilon}$ the Dirichlet-Neumann Laplacian in $\Omega_\varepsilon$. In this work, we study the spectral problem of $-\Delta_{DN}^{\Omega_\varepsilon}$. The asymptotic behaviour for the non-decreasing sequence of numbers $\{\lambda_j(-\Delta_{DN}^{\Omega_\varepsilon})\}_{j=1}^{\infty}$ given by Max–Min Principle will be obtained, under the condition that $\Omega_\varepsilon$ is thin enough. Furthermore, we study the spectral properties of the Dirichlet-Neumann Laplacian in a thin strip of a fixed width.
Spectrum of the Dirichlet-Neumann Laplacian in a thin strip
Keywords: Operador Laplaciano; Condições de Dirichlet-Neumann; Formas quadráticas; Espectro essencial; Espectro discreto; Faixas estreitas; Laplacian operator; Dirichlet-Neumann boundary conditions; Quadratic forms; Essential spectrum; Discrete spectrum; Thin strips; CIENCIAS EXATAS E DA TERRA::MATEMATICA::ANALISE::ANALISE FUNCIONAL; CIENCIAS EXATAS E DA TERRA::MATEMATICA; CIENCIAS EXATAS E DA TERRA::MATEMATICA::ANALISE