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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 ...
Unicidade para equações dos tipos: Burgers, Kuramoto-Sivashinsky e Schrödinger
(Universidade Federal de São Carlos, 2017-12-15)
Based on Carleman's estimates and under certain conditions of linear exponential decay we prove uniqueness for equations of type: Burgers, Kuramoto-Sivashinsky and Schrödinger.
Superfícies mínimas e a teoria min-max de Almgren--Pitts
(Universidade Federal de São Carlos, 2019-08-07)
First, we introduce the basic concept of minimal surfaces and develop some results in the general theory of minimal surfaces.
In the second part, we are interested in the Simon-Smith Min-Max approach to prove the existence ...
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 ...
Fluxo de curvatura média e self-shrinkers
(Universidade Federal de São Carlos, 2020-06-12)
Mean curvature flow is a geometric flow that rises when evolving a hipersurface in the direction of its normal vector field with velocity at each point equal to the mean curvature at the very same point. As it is an evolution ...
Espectro do Laplaciano de Dirichlet-Neumann em faixas estreitas
(Universidade Federal de São Carlos, 2020-08-11)
Let $\Omega_\varepsilon$ be a thin strip in $\mathbb{R}^2$ and $-\Delta_{DN}^{\Omega_\varepsilon}$ the Dirichlet-Neumann Laplacian in $\Omega_\varepsilon$. In this work, we study the spectral problem of $-\Delta_{DN}^{\O ...
Uma estimativa do tipo L1 para potencial de Riesz
(Universidade Federal de São Carlos, 2019-08-13)
In this work we will present a L1-type estimates for the Riesz potentials envolving the Riesz transform. This estimate is an improvement of result due to Stein and Weiss the result of Stein and Weiss that provides Riesz ...
Efeito Aharonov-Bohm sem interação com a fronteira do solenóide
(Universidade Federal de São Carlos, 2013-03-08)
One of the biggest problem in the mathematical modeling of the Aharonov- Bohm Effect is the interaction between the electron and the solenoid border. Such interaction translates into boundary conditions on that border, ...