Uma versão Lipschitz do teorema de Sard

• Ano de defesa: 2021
• Autor(a) principal: Rocha, André Gadelha
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Palavras-chave em Português: Conjuntos subanalíticos; Análise convexa; Teorema de Sard Lipschitz; Derivada de Clarke; Subanalytic sets; Convex analysis; Sard Lipschitz's theorem; Clarke's derivative
• Link de acesso: http://www.repositorio.ufc.br/handle/riufc/63315

The aim of this work is to study a Lipschitz version of Sard’s Theorem. In relation to the Sard Theorem in its classic version, we will change the hypothesis of being C1 for subanalytic and locally Lipschitz. Since we are not necessarily working with differentiable functions, the critical points will be replaced by Clarke’s critical points. Finally, we will give examples which show that the theorem is not true, if we omit the locally Lipschitz hypothesis or the subanalytic hypothesis.