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Invariantes de singularidades em característica positiva
(Universidade Federal de São Carlos, 2020-03-30)
This dissertation mainly follows the works of \cite{Gr2} and \cite{Gr5}.
Considering $\mathbb{K}$ a field, algebraically closed with positive characteristic, we presented invariants of singularities in $\mathbb{K}[[\u ...
Representação de soluções homogêneas contínuas de campos vetoriais no plano
(Universidade Federal de São Carlos, 2015-06-11)
In this work we study conditions for the validity of the analogue of Mergelyan’s
theorem for continuous solutions of a type of locally integrable vector field.
On a domain in the plane, we consider a vector field L that ...
Mínimos locais de funcionais com dependência especial via Γ-convergência: com e sem vínculo
(Universidade Federal de São Carlos, 2011-05-30)
We address the question of existence of stationary stable solutions to a class of reaction-diffusion equations with spatial dependence in 2 and 3-dimensional bounded domains. The approach consists of proving the existence ...
Aplicações singulares via grupos de reflexões
(Universidade Federal de São Carlos, 2020-04-24)
Our objective with this essay is to describe a way to build germs of applications A-finite f:(\C^{n},0) \rightarrow (\C^{p},0) for p=2n and p=2n-1. In the case p<2n-1, we conclude that there is no germ of reflection ...
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 ...
Teoria dos operadores integrais singulares
(Universidade Federal de São Carlos, 2020-04-28)
We present in this work some of the main results regarding the continuity in Lp and the definition almost everywhere of operators known as Singular Integrals, as well as some classic examples and applications. We have ...
Extensões auto-adjuntas do operador de Schrödinger magnético em domínios com pouca regularidade
(Universidade Federal de São Carlos, 2020-02-20)
We find one parametrization of all self-adjoint extensions of the magnetic Schrödinger
operator, in a quasi-convex domain with compact boundary, and magnetic potentials
with low regularity. In this parametrization we use ...
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 ...
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 ...
Sobre a metrizabilidade do espaço de R-lugares de um corpo de funções F com trdeg_R=1
(Universidade Federal de São Carlos, 2020-02-28)
The main purpose of this work is to study the metrizability of the space of R-places of a function field, with transcendence degree 1 over a real closed field. Specifically, we are going to present a necessary and sufficient ...