DSpace Coleção:
http://www.repositorio.ufc.br/handle/riufc/65
Mon, 17 Jun 2019 03:35:12 GMT2019-06-17T03:35:12ZSharp and improved regularity estimates to fully nonlinear equations and free boundary problems.
http://www.repositorio.ufc.br/handle/riufc/41839
Título: Sharp and improved regularity estimates to fully nonlinear equations and free boundary problems.
Autor(es): Silva, João Vitor da
Abstract: The thesis consists of the following three papers on regularity estimates for fully non-linear parabolic equations and one-phase singularly perturbed elliptic problems. Sharp regularity estimates for second order fully nonlinear parabolic equations - Joint work with Eduardo V. Teixeira. The purpose of the fi rst chapter is prove sharp regularity estimates for viscosity solutions to fully non-linear parabolic equations of the form
@u@t F(D2u; Du; x; t) = f(x; t) in Q 1 = B 1 ( 1; 0]; (Eq1) where F is a uniformly elliptic operator and f 2 L p;q (Q 1 ). The quantity (n; p; q) :=np+2q determines which regularity regime a solution to (Eq1) belongs to. We prove that when 1 < (n; p; q) < 2 ϵ F , solutions are parabolic-Hölder continuous for a sharp, quantitative exponent 0 < (n; p; q) < 1. The case (n; p; q) = 1 is a critical borderline situation as it divides the regularity theory. In this scenario, we obtain a sharp universal Log-Lipschitz regularity estimate. When 0 < (n; p; q) < 1, solutions are locally of class C 1+ ;1+ 2 and in the limiting case (n; p; q) = 0, we show C 1;Log-Lip regularity estimates provided F is convex in the Hessian argument for example. Schauder Type Estimates for “Flat” Viscosity Solutions to Non-convex Fully Nonlinear Parabolic Equations and Applications - Joint work with Disson S. dos Prazeres. In a second moment we establish Schauder type estimates for fl at solutions to non-convex fully non-linear parabolic equations of the following form @u@t F(x; t; D2u) = f(x; t) in Q 1 (Eq2) provided the coeffi cientsof F and the source f are Dini continuous. Furthermore, we prove a partial regularity result, as well as a theorem of Evans-Krylov type. Finally, for problems with merely continuous data we prove that fl at solutions to( Eq2) are parabolic C 1;Log-Lip smooth. Regularity up to the boundary for fully nonlinear singularly perturbed elliptic equations - Joint work with Gleydson C. Ricarte. Posteriorly, we are interested in studying regularity up to the boundary for one-phasesingularly perturbed fully non-linear elliptic problems F(x; Du"; D2u") = ϵ (uϵ) in Ω R n (Eq3) where " behaves asymptotically as the Dirac measure 0 as " goes to zero. We shall establish global gradient bounds independent of the parameter " to viscosity solutions to (Eq3), which allow us to pass the limit and obtain optimal regularity for free boundary problem.Mon, 23 Mar 2015 00:00:00 GMThttp://www.repositorio.ufc.br/handle/riufc/418392015-03-23T00:00:00ZUm teorema tipo-Picard para a aplicação de Gauss hiperbólica de superfícies CMC-1 imersas no espaço hiperbólico e no espaço de Sitter 3-dimensional.
http://www.repositorio.ufc.br/handle/riufc/41791
Título: Um teorema tipo-Picard para a aplicação de Gauss hiperbólica de superfícies CMC-1 imersas no espaço hiperbólico e no espaço de Sitter 3-dimensional.
Autor(es): Andrade, Nícolas Alcântara de
Abstract: In this work we study the hyperbolic Gauss map of CMC-1 immersed surfaces in hyperbolic 3-space, also known as Bryant surfaces, and of CMC-1 faces in the de Sitter 3-space. We obtain a sharp estimate of the missing points of this map when the surface has ﬁnite total curvature, providing a Picard-type theorem for hyperbolic Gauss map in these spaces.Tue, 08 Jan 2019 00:00:00 GMThttp://www.repositorio.ufc.br/handle/riufc/417912019-01-08T00:00:00ZA massa em termos dos tensores de Einstein e Newton e aplicações.
http://www.repositorio.ufc.br/handle/riufc/40947
Título: A massa em termos dos tensores de Einstein e Newton e aplicações.
Autor(es): Sayago, Amilcar Montalban
Abstract: It is shown that the mass and the center of mass of an asymptotically ﬂat Riemannian manifold with noncompact boundary can be computed as the limit, as r goes to inﬁnity, of the integral, over the coordinate sphere of radius r, of expressions in terms of the Einstein and Newton tensors of the manifold. The expression obtained for the mass is then used to give a new proof, for noncompact Euclidean graphs, of the positive mass theorem and the Penrose inequality.Tue, 26 Mar 2019 00:00:00 GMThttp://www.repositorio.ufc.br/handle/riufc/409472019-03-26T00:00:00ZEstimativas de fronteira para problemas elípticos de perturbação singular na teoria de combustão
http://www.repositorio.ufc.br/handle/riufc/40357
Título: Estimativas de fronteira para problemas elípticos de perturbação singular na teoria de combustão
Autor(es): Silva, José Gleison Carneiro da
Abstract: In this work we study up to the boundary Lipschitz estimates for classes of singular perturbation problems appearing in the combustion theory in the study of ﬂame propagation issues. Here we study problems involving the fully nonlinear equation and quasilinear type equations both involving unbounded force terms (RHS).Fri, 12 Feb 2016 00:00:00 GMThttp://www.repositorio.ufc.br/handle/riufc/403572016-02-12T00:00:00Z