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Heat equation and the Yamabe flow on manifolds with fibered boundary metric
(Universidade Federal de São Carlos, 2021-09-02)
This work is dedicated to the study of the Yamabe flow on a class of non-compact complete Riemannian manifolds with fibered boundary and infinite volume, called Phi-manifolds. Some examples of this type of manifold include ...
A álgebra graduada associada a uma valorização
(Universidade Federal de São Carlos, 2021-11-30)
We begin this work with a study of the graded algebra associated to a valuation $\nu: K \longrightarrow \Gamma_{\infty}$. We verify that in the cases where the value group is free or the residue field is closed by radicals, ...
Espaços de Hardy radial
(Universidade Federal de São Carlos, 2020-02-06)
One presents in this work an atomic decomposition via radial atoms for distributions on subspace $\mathcal{H}^{p}_{rad}(\mathds{R}^{n})$ for $0 < p\leqslant 1$, of Hardy radial spaces $H_{rad}^{p}(\mathds{R}^{n}) \doteq ...
Existence and multiplicity of solutions for a class of elliptic equations involving nonlocal integrodifferential operator with variable exponent
(Universidade Federal de São Carlos, 2020-03-16)
In this work, we are interested in the existence and multiplicity of nontrivial solutions for a class of elliptic problems. The first problem deals with the existence of nontrivial weak solutions to a class of elliptic ...
Equisingularidades de funções definidas em ICIS e IDS
(Universidade Federal de São Carlos, 2020-03-10)
We study the equisingularity of a family of function germs $\{f_t\colon(X_t,0)\to (\mathbb{C},0)\}$, where $\{(X_t,0)\}$ is a family of $d$-dimensional isolated determinantal singularity. We define the $(d-1)$th polar ...
Grafeno multicamadas através de grafos quânticos periódicos: cones de Dirac
(Universidade Federal de São Carlos, 2020-03-06)
We study the spectral characterization and Dirac cones, always through periodic quantum graphs, in three situations. Firstly, we model bidimensional honeycomb materials, for instance, Graphene and Boron Nitride. We consider ...
Boa postura para alguns sistemas de equações dispersivas e para uma equação dispersiva
(Universidade Federal de São Carlos, 2020-10-30)
The main aim of this work is to establish the well posedness for a dispersive partial differential equations systems and for a partial differential equation, with initial data belonging to Gevrey space.
The proof ...
Três resultados de sistemas dinâmicos em dimensões baixas
(Universidade Federal de São Carlos, 2020-12-18)
This work contains three independent results that can be framed within the research
area named low-dimensional dynamics. The first result is a lower bound for the maximal
number of inseparable leaves of non-singular ...
Boa postura analítica e Gevrey da “boa” equação de Boussinesq
(Universidade Federal de São Carlos, 2021-03-11)
In both the line and the circle, we shall to prove that the Cauchy problem for the ``good'' Boussinesq equation is locally well-posed in a class of Gevrey functions, which includes a class of analytic functions that can ...
Sobre teoremas do tipo Tverberg
(Universidade Federal de São Carlos, 2020-12-17)
The main objective of this work is to prove Tverberg-type theorems and related results. More specifically, we will present an alternative proof for the Bárány-Larman conjecture for the case $r = p-1 $ with $ p $ a prime, ...