https://repositorio.ufpb.br/jspui/handle/tede/6873 PPGMAT 2026-05-02T08:10:23Z https://repositorio.ufpb.br/jspui/handle/123456789/37773 Título: Sobre uma desigualdade do tipo Hardy-Sobolev e aplicações Autor(es): Lima, Francisco Jonatã Chaves de Orientador: Medeiros, Everaldo Souto de Abstract: In this work, we present a Hardy-Sobolev type inequality in cylindrical domains and, as a consequence, derive some Sobolev embeddings into weighted Lebesgue spaces. We prove that the attainability of the best constant for these weighted embeddings is equivalent to establishing the existence of ground state solutions for a class of elliptic problems in R. Regularity and behavior of the minimizers are also analyzed. As an application of the obtained embeddings, we prove existence and non-existence results for a class of elliptic problems with critical growth. Editor: Universidade Federal da Paraíba Tipo: Dissertação 2025-02-19T00:00:00Z https://repositorio.ufpb.br/jspui/handle/123456789/37772 Título: Uma introdução às variedades tóricas Autor(es): Lima, Fagner da Silva Orientador: Pereira, Miriam da Silva Abstract: In this work, we studied about affine toric varieties related to polyhedral lattice cones that are strongly convexes. From the collage of these varieties, we defined the toric variety, as well as describing some of their properties. Besides, we analyzed the action of the algebraic torus in the toric varieties in order to describe their orbits. Editor: Universidade Federal da Paraíba Tipo: Dissertação 2018-03-20T00:00:00Z https://repositorio.ufpb.br/jspui/handle/123456789/37655 Título: Estimativas de Schauder Autor(es): Silva, Robson Lucas Soares da Orientador: Araújo, Damião Júnio Gonçalves Abstract: In this work, we study regularity of solutions of second order PDE’s. More precisely, we study universal C 2,α regularity estimates of solutions, which are also known as Schauder estimates. We divide the thesis in three parts: in the first part, we study results of C 2,α solutions of Poisson Equations which are a-priori α-H ̈older continuous. In the second part, we study C 2,α regularity of solutions of linear second order elliptic PDE’s, with C α coefficients, through an interior estimate. Finally, we study the C 2,α regularity of viscosity solutions of fully non-linear second order elliptic PDE’s. Editor: Universidade Federal da Paraíba Tipo: Dissertação 2020-07-24T00:00:00Z https://repositorio.ufpb.br/jspui/handle/123456789/37654 Título: Desigualdades de Bohnenblust-Hille, de Hardy-Littlewood e de Khinchin Autor(es): Santos, Djair Paulino dos Orientador: Pellegrino, Daniel Marinho Abstract: In this work we present variations of three classical inequalities and we investigate the corresponding optimal constants and exponents. In Chapter 1 we prove a multilinear version of the BohnenblustHille inequality for uniformly bounded indexes; In Chapter 2 we prove HardyLittlewood like inequalities for m-linear forms T : `p1 ×· · ·×`pm −→ K in the case 1/p1 + · · · + 1/pm ≥ 1, which until then have never been investigated for technical reasons. Finally, in Chapter 3 we present variations of the multiple Khinchin inequality. Editor: Universidade Federal da Paraíba Tipo: Tese 2020-10-05T00:00:00Z