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The Dirichlet problem for elliptic and degenerate elliptic equations, and related results
(University of Missouri--Columbia, 2016)
In this thesis, we first prove the solvability of Dirichlet problem with Lp data on the boundary for degenerate elliptic equations. Second, We obtain Lp bounds semi-groups and their gradients, and then we get Lp bounds for ...
Some results in convex geometry
(University of Missouri--Columbia, 2016)
This thesis is divided into four parts. The first part is about proving that the unit ball of the Lorentz space is not an intersection body for dimension greater than or equal to 5 and q > 2. We go on to explain the ...
On hydrodynamic equations and their relation to kinetic theory and statistical mechanics
(University of Missouri--Columbia, 2017)
[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] We establish conditions on the Hamiltonian evolution of interacting molecules that imply hydrodynamic equations at the limit of infinitely many molecules ...
Topics in harmonic analysis and partial differential equations: extension theorems and geometric maximum principles
(University of Missouri--Columbia, 2011)
The present thesis consists of two main parts. In the first part, we prove that a function defined on a closed subset of a geometrically doubling quasi-metric space which satisfies a Hölder-type condition may be extended ...
Outer products and frame coefficients /
(University of Missouri--Columbia, 2017)
In this dissertation, we will examine two distinct areas of frame theory. The first will be the area of outer products. In particular, we will examine the spanning and independence properties of the collection [see abstract ...
Endpoint solvability results for divergence form, complex elliptic equations
(University of Missouri--Columbia, 2011)
We consider divergence form elliptic equations Lu := ∇ • (A∇u) = 0 in the half space ℝn+1+ := {(x,t)∈ ℝn x (0,∞)}, whose coeffi cient matrix A is complex elliptic, bounded and measurable. In addition, we suppose that A ...
Nonlinear equations with natural growth terms
(University of Missouri--Columbia, 2011)
This thesis concerns the study of a class of second order quasilinear elliptic differential operators. For 1 < p < ∞, the model equation we consider is: (1) L(u) = -Δpu - σ∣u∣p-2u. Here the potential is a function (or ...
Results in analytic and algebraic number theory
(University of Missouri--Columbia, 2012)
The thesis begins with proving some theorems about Gauss sums and Jacobi sums. Using theorems the first chapter ends with a proof that if p is a prime such that p ≡ 1 (mod 4), then there are integers a and b such that p = ...
Generalized local Tb theorem and applications
(University of Missouri--Columbia, 2012)
The Tb theorem, like its predecessor, the T1 Theorem, is an L2 boundedness criterion, originally established by McIntosh and Meyer, and by David, Journé and Semmes in the context of singular integrals, but later extended ...
Quasi-metric geometry
(University of Missouri--Columbia, 2014)
two objects is one of the most fundamental and ubiquitous in many branches of mathematics. A quasi-metric is a generalization of the familiar notion of metric. This dissertation examines what happens in this new setting of quasi-metrics. In particular...
Dichotomy theorems for evolution equations
(University of Missouri--Columbia, 2008)
[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] In the first part of this work, under minimal assumptions, we characterize the Fredholm property and compute the Fredholm index of abstract differential ...
Geometric and nonlinear limit theorems in probability theory
(University of Missouri--Columbia, 2012)
The concentration of measure phenomenon is a nonlinear equivalent of the law of large numbers that deals with real valued Lipschitz functions and includes linear functionals such as the sample mean. In the first part of ...
Coefficient theorems of Birancon-Skoda type
(University of Missouri--Columbia, 2011)
[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] The original Briancon-Skoda theorem, proved for the ring of convergent power series over the field $mathbb{C}$ of complex numbers, was later generalized ...
Minimal homogeneous resolutions, almost complete intersections and Gorenstein Artin algebras
(University of Missouri--Columbia, 2011)
[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] This work is devoted to the study of the structures of the graded resolutions of codimension three almost complete intersections and the unimodality ...
Complemented block bases of symmetric bases and spectral tetris fusion frame constructions
(University of Missouri--Columbia, 2012)
[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] This work contains of two parts which are totally unrelated. In the first part we consider techniques surrounding the problem whether a complemented ...
Stability and instability results for the 2D [alpha]-Euler equations /
(University of Missouri--Columbia, 2017)
We study stability and instability of time independent solutions of the two dimensional a-Euler equations and Euler equations; the a-Euler equations are obtained by replacing the nonlinear term (u [times] [del.])u in the ...
On the periodicity of the first Betti number of the semigroup ring under translations
(University of Missouri--Columbia, 2010)
eventually with period a+b+c.4) Let X*=(a,b,p(a+b)) or X*=(p(b+c),b,c). If the first Betti number of P* is 3 then (a+b+c) divides j+1.--From public.pdf....
Toroidalization of locally toroidal morphisms
(University of Missouri--Columbia, 2008)
Let X and Y be nonsingular varieties over an algebraically closed field [kappa] of characteristic zero. A toroidal structure on X is a simple normal crossing divisor DX on X. Suppose that DX and DY are toroidal structures ...
Mathematical and computational modeling of fluid flow with applications in ophthalmology and geoscience
(University of Missouri--Columbia, 2020)
[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] Complex systems in our life can be translated to mathematical models whose solutions can help us to predict the behavior of the system. Disease in eye and internal erosion...
Box approximation and related techniques in spectral theory
(University of Missouri--Columbia, 2008)
This dissertation is concerned with various aspects of the spectral theory of differential and pseudodifferential operators. It consists of two chapters. The first chapter presents a study of a family of spectral shift ...