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ExistÃncia e unicidade para os problemas de Dirichlet e Neumann sobre um domÃnio com fronteira suave / Existence and uniqueness for the Dirichlet and Neumann problems on a domain with smooth boundaryCÃcero Fagner Alves da Silva 08 July 2010 (has links)
CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel Superior / Seja Ω um domÃnio fixado em Rn com fronteira S de classe C2 e denote Ω′ = Rn Ω. Ambos Ω e Ω′ nÃo necessariamente conexos. Nessas condiÃÃes, pretendemos resolver os problemas de Dirichlet e Neumann.
No intuito da resoluÃÃo dos problemas citados, faremos um estudo daTeoria de Fredholm (operadores compactos), bem como da transformada de Kelvin, harmonicidade no infinito e dos potenciais de camada. / Let Ω be a fixed domain in Rn with boundary S of class C2 and denote Ω′ = Rn Ω. Both Ω and Ω′ not necessarily connected. Under these conditions, we intend to solve the problems of Dirichlet and Neumann.
In order to overcome the mentioned the problems, we will study the Fredholm theory (compact operators), the Kelvin transformed, harmonicity in the infinite and potential of the layer.
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The Eigensolutions of the balance equations over a sphere.Moura, Antônio Divino January 1975 (has links)
Thesis. 1975. Ph.D.--Massachusetts Institute of Technology. Dept. of Meteorology. / Vita. / Bibliography: leaves 168-170. / Ph.D.
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Gauss-type formulas for linear functionalsChen, Jih-Hsiang January 1982 (has links)
We give a method, by solving a nonlinear system of equations, for Gauss harmonic interpolation formulas which are useful for approximating, the solution of the Dirichlet problem.
We also discuss approximations for integrals of the form
I(f) = (1/2πi) ∫<sub>L</sub> (f(z)/(z-α)) dz.
Our approximations shall be of the form
Q(f) = Σ<sub>k=1</sub><sup>n</sup> A<sub>k</sub>f(τ<sub>k</sub>).
We characterize the nodes τ₁, τ₂, …, τ<sub>n</sub>, to get the maximum precision for our formulas.
Finally, we propose a general problem of approximating for linear functionals; our results need further development. / Ph. D.
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Maxwell’s Problem on Point Charges in the PlaneKillian, Kenneth 19 June 2008 (has links)
This paper deals with approximating an upper bound for the number of equilibrium points of a potential field produced by point charges in the plane. This is a simplified form of a problem posed by Maxwell [4], who considered spatial configurations of the point charges. Using algebraic techniques, we will give an upper bound for planar charges that is sharper than the bound given in [6] for most general configurations of charges. Then we will study an example of a configuration of charges that has exactly the number of equilibrium points that Maxwell's conjecture predicts, and we will look into the nature of the extremal points in this case. We will conclude with a solution to the twin problem for the logarithmic potential, followed by a discussion of the conditions necessary for a degenerate case in the plane.
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Paley-Wiener theorem and Shannon sampling with the Clifford analysis settingKou, Kit Ian January 2005 (has links)
University of Macau / Faculty of Science and Technology / Department of Mathematics
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Entire Solutions to Dirichlet Type ProblemsSitar, Scott January 2007 (has links)
In this thesis, we examined some Dirichlet type problems of
the form:
\begin{eqnarray*}
\triangle u & = & 0\ {\rm in\ } \mathbb{R}^n \\
u & = & f\ {\rm on\ } \psi = 0,
\end{eqnarray*}
and we were particularly interested in finding entire solutions
when entire data was prescribed. This is an extension of the work
of D. Siegel, M. Mouratidis, and M. Chamberland, who were interested
in finding polynomial solutions when polynomial data was prescribed.
In the cases where they found that polynomial solutions always existed
for any polynomial data, we tried to show that entire
solutions always existed given any entire data. For half space
problems we were successful, but when we compared this to the heat
equation, we found that we needed to impose restrictions on the type
of data allowed. For problems where data is prescribed on a pair of
intersecting lines in the plane, we found a surprising dependence
between the existence of an entire solution and the number
theoretic properties of the angle between the lines. We were
able to show that for numbers $\alpha$ with $\omega_1$ finite
according to Mahler's classification of transcendental numbers,
there will always be an entire solution given
entire data for the angle $2\alpha\pi$ between the lines.
We were also able to construct an uncountable, dense set of
angles of measure 0, much in the spirit of Liouville's number,
for which there will not always be an entire solution for all
entire data.
Finally, we investigated a problem where data is given
on the boundary of an infinite strip in the plane. We were unable to settle
this problem, but we were able to reduce it to other
{\it a priori} more tractable problems.
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Entire Solutions to Dirichlet Type ProblemsSitar, Scott January 2007 (has links)
In this thesis, we examined some Dirichlet type problems of
the form:
\begin{eqnarray*}
\triangle u & = & 0\ {\rm in\ } \mathbb{R}^n \\
u & = & f\ {\rm on\ } \psi = 0,
\end{eqnarray*}
and we were particularly interested in finding entire solutions
when entire data was prescribed. This is an extension of the work
of D. Siegel, M. Mouratidis, and M. Chamberland, who were interested
in finding polynomial solutions when polynomial data was prescribed.
In the cases where they found that polynomial solutions always existed
for any polynomial data, we tried to show that entire
solutions always existed given any entire data. For half space
problems we were successful, but when we compared this to the heat
equation, we found that we needed to impose restrictions on the type
of data allowed. For problems where data is prescribed on a pair of
intersecting lines in the plane, we found a surprising dependence
between the existence of an entire solution and the number
theoretic properties of the angle between the lines. We were
able to show that for numbers $\alpha$ with $\omega_1$ finite
according to Mahler's classification of transcendental numbers,
there will always be an entire solution given
entire data for the angle $2\alpha\pi$ between the lines.
We were also able to construct an uncountable, dense set of
angles of measure 0, much in the spirit of Liouville's number,
for which there will not always be an entire solution for all
entire data.
Finally, we investigated a problem where data is given
on the boundary of an infinite strip in the plane. We were unable to settle
this problem, but we were able to reduce it to other
{\it a priori} more tractable problems.
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A numerical scheme for Mullins-Sekerka flow in three space dimensions /Brown, Sarah M. January 2004 (has links) (PDF)
Thesis (Ph. D.)--Brigham Young University. Dept. of Mathematics, 2004. / Includes bibliographical references (p. 113-117).
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The application of RV Southwells' relaxation methods to the solution of problems in torsion of prismatic barsLeitner, Murray Irving, 1922- January 1949 (has links)
No description available.
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Generalizations of a result of Lewis and Vogel /Kissel, Kris. January 2007 (has links)
Thesis (Ph. D.)--University of Washington, 2007. / Vita. Includes bibliographical references (p. 85-86).
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