DSpace Coleção:
http://www.repositorio.ufc.br/handle/riufc/65
2018-10-20T17:40:15ZSingular perturbation methods and optimal regularity for degenerate equations.
http://www.repositorio.ufc.br/handle/riufc/35141
Título: Singular perturbation methods and optimal regularity for degenerate equations.
Autor(es): Araújo, Janielly Gonçalves
Abstract: In the ﬁrst part of this work we prove interior and up to boundary Lipschitz regularity of the viscosity solutions to a singular perturbation problem for a reaction-diﬀusion equation related to the normalized p-Laplacian equation |∇u | 2−p · div |∇u | p−2 ∇u = β (u ), where the reaction term is of combustion type. We obtain the precise geometric behavior of solutions near -level surfaces, by means of optimal regularity and sharp geometric nondegeneracy. We pass to the limit we investigate Hausdorﬀ measure properties of the
limit function. In the second part the aim is to obtain sharp regularity estimates for locally bounded solutions of the degenerate doubly nonlinear equation u t − div(m|u| m−1 |∇u| p−2 ∇u) = f, where m > 1, p > 2 and f ∈ L q,r . More precisely, we show that solutions are locally of class C 0,β , where β depends explicitly only on the optimal H¨older exponent for solutions of the homogeneous case, the integrability of f, the constants p, m and the space dimension n.
Descrição: ARAÚJO, Janielly Gonçalves. Singular perturbation methods and optimal regularity for degenerate equations. 2018. 78 f. Tese (Doutorado em Matemática) – Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2018.2018-07-26T00:00:00ZDirichlet problems for mean curvature and p-harmonic equations on Cartan-Hadamard manifolds.
http://www.repositorio.ufc.br/handle/riufc/34925
Título: Dirichlet problems for mean curvature and p-harmonic equations on Cartan-Hadamard manifolds.
Autor(es): Heinonen, Esko Antero
Abstract: The unifying theme of the ﬁve articles, [A,B,C,D,E], forming this dissertation is the existence and non-existence of continuous entire non-constant solutions for nonlinear diﬀerential operators on a Riemannian manifold M. The existence results of such solutions are proved by studying the asymptotic Dirichlet problem under diﬀerent assumptions on the geometry of the manifold. Minimal graphic functions are studied in articles [A] and [D]. Article [A] deals with an existence result whereas in [D] we give both existence and non-existence results with respect to the curvature of M. Moreover p-harmonic functions are studied in [D]. Article [B] deals with the existence of A -harmonic functions under similar curvature assumptions as in [A]. In article [C] we study the existence of f-minimal graphs, which are generalisations of usual minimal graphs, and in the article [E] the Killing graphs on warped product manifolds. Before turning to the ideas and results of the research articles, we present some key concepts of the thesis and give a brief history of the development of the asymptotic Dirichlet problem. Due to the similarity of the techniques in [A] and [B], we treat them together in Section 3. Article [C] is treated in Section 4, article [D] in Section 5 and article [E] in Section 6. At the beginning of the Sections 3 – 6 we brieﬂy give the background of the methods and techniques used in the articles.
Descrição: HEINONEN, Esko Antero. Dirichlet problems for mean curvature and p-harmonic equations on Cartan-Hadamard manifolds. 2018. 166 f. Tese (Doutorado em Matemática) – Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2018.2018-03-06T00:00:00ZMétricas críticas do funcional volume fracamente Einstein e variedades com tensores de divergência nula
http://www.repositorio.ufc.br/handle/riufc/34307
Título: Métricas críticas do funcional volume fracamente Einstein e variedades com tensores de divergência nula
Autor(es): Oliveira, Fabricio de Figueredo
Abstract: We studied critical points of the functional volume in onboard varieties and the functional total scalar curvature in varieties with no board. We prove that under a signal condition in the scalar curvature and with the hypothesis that an n dimensional manifold is weakly Einstein it is possible to classify Miao-Tam Critical Metrics as geodesic balls in shape spaces. Then we prove that the Cotton tensor is always zero when there is zero divergence and we improve some classic results on the CPE conjecture like Yun (2014) besides giving a simpler proof than Santos (2017) for the CPE conjecture when the second divergence of Weyl is null.
Descrição: OLIVEIRA, F. F. Métricas críticas do funcional volume fracamente Einstein e variedades com tensores de divergência nula. 2018. 54 f. Tese (Doutorado em Matemática) – Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2018.2018-01-01T00:00:00ZImersões isométricas k-umbílicas em formas espaciais
http://www.repositorio.ufc.br/handle/riufc/31877
Título: Imersões isométricas k-umbílicas em formas espaciais
Autor(es): Echaiz-Espinoza, Fernando Enrique
Abstract: Let x be an isometric immersion in its second fundamental form. Newton's polynomials are defined inductively by Po = I, Pk = Sk I-A Pk-1, where Sk is the immersion k-curvature. This work defines k-umbilicity by the proviso that the product of A by the Newton polynomial of k-1 is a multiple of identity. As a general consequence of the k-umbilicity concept, it is shown that if a k-umbilical isometric immersion has a zero main curvature, then it has n-k + 1 null principal curvatures and also shows that in every k-umbilical immersion the perk Lk is elliptical whenever Sk is nonzero, considering Lk (f) = dash (Pk Hess (f)) a second-order differential operator. For the case k = 2, it shows that all 2-umbilical immersion in spatial forms has S2 constant. It also partially classifies the closed 2-umbilical hypersurfaces on the unit sphere, exhibiting an enumerable family of such immersions.
Descrição: Echaiz-Espinoza, Fernando Enrique. Imersões isométricas k-umbílicas em formas espaciais. 2004. 129 f. Tese (Doutorado em Matemática)- Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2004..2004-02-10T00:00:00Z