Parabolic equations on conic manifolds

• Autor(a) principal: Sulez, Weymar Andrés Astaiza
• Data de Publicação: 2024
• Tipo de documento: Tese
• Idioma: eng
• Título da fonte: Biblioteca Digital de Teses e Dissertações da USP
• Texto Completo: https://www.teses.usp.br/teses/disponiveis/45/45132/tde-05042024-204731/
• topic: Conic manifolds; Espaços Mellin-Sobolev; Mellin-Sobolev spaces; Operadores pseudodiferenciais; Operadores setoriais e quase setoriais; Pseudodifferential operators; Sectorial and almost sectorial operator; Variedades cônicas

We are going to present results about parabolic equations on conic manifolds using Lp and continuous functions. First, we show existence of global solutions for a typical Reaction-Diffusion equation on a conic manifold B. We consider Mellin-Sobolev spaces. These are function spaces built using Lp norms. Second, we show sectoriality for elliptic differential and pseudodifferential operators acting on continuous spaces on compact manifolds without boundary and without conical points. Third, for a conic manifold B, we extend the continuous and C1 spaces and we show that elliptic differential operators define almost sectorial operators on these spaces.