Propriedades de autovalores para uma classe de operadores elìpticos de segunda ordem

• Ano de defesa: 2016
• Autor(a) principal: Cunha, Cleiton Lira
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: por
• Palavras-chave em Português: Fórmula variacional tipo Hadamard; Fluxo de Ricci; Condições de bordo de Dirichlet; Condições de bordo de Neumann
• Link de acesso: http://www.repositorio.ufc.br/handle/riufc/21166

We deal with properties of eigenvalues of a class of elliptic operators in the divergence form on a compact Riemannian manifold M, which we denote by L. When the metric varies analytically on M, we obtain analytic curves of eigenvalues and eigenfunctions of L satisfy Dirichlet boundary condition. We compute Hadamard type variational formula and as application we show that the set of Cr{metrics, such that L has simple spectrum, is a generic set. We prove that the set of Cr{di eomorphisms on a domain in M such that the eigenvalues of L are simples is a generic property too. We also analysis the behavior of eigenvalues when the metric varies through Ricci ow in closed Riemannian manifold, showing, for example, that it increase under suitable hypothesis. We still show that the results of genericity are valid under Neumann boundary condition.