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#### Potential theory and harmonic analysis methods for quasilinear and Hessian equations

(University of Missouri--Columbia, 2006)

The existence problem is solved, and global pointwise estimates of solutions are obtained for quasilinear and Hessian equations of Lane-Emden type, including the following two model problems:-[delta]pu = uq + [

**mu**], Fk[-u] = uq + [**mu**], u [greater...#### Trace formulae in finite von Neumann algebras

(University of Missouri--Columbia, 2007)

The dissertation is devoted to some aspects of spectral perturbation theory in the context of finite Von Neumann algebras. The central results are analogs of the Birman-Schwinger principle and the Birman-Krein formula for ...

#### Capillary-gravity water waves with vorticity : steady wind-driven waves and waves with a submerged dipole

(University of Missouri--Columbia, 2019)

In this thesis, we study two mathematical problems on water waves in the setting of the incompressible Euler equations with vorticity, gravity, and surface tension. We investigate the existence of small-amplitude steady ...

#### Toroidalization of locally toroidal morphisms

(University of Missouri--Columbia, 2008)

[arrow] Y1 is toroidal. Let [function] : X [arrow] Y be a dominant morphism. Suppose that there exist finite open covers (Ui) and (Vi) of X and Y respectively such that [function] (Ui) [arrow] Vi and the

**restricted**morphisms [function] : (Ui) [arrow] Vi...#### The implicit function theorem for Lipschitz functions and applications

(University of Missouri--Columbia, 2008)

The subject matter of this thesis is the classical Implicit Function Theorem and its generalizations. Dictated by practical applications, it is of interest to relax the hypothesis of the standard Implicit Function Theorem ...

#### A free boundary gas dynamic model as a two-body field theory problem

(University of Missouri--Columbia, 2009)

Motivated by the two-body problem in the classical field theories of electrodynamics and gravitation, in which finite propagation speeds lead to radiation reaction and runaway solutions, we develop a free boundary problem ...

#### Persistent homology : categorical structural theorem and stability through representations of quivers

(University of Missouri--Columbia, 2018)

The purpose of this thesis is to advance the study and application of the field of persistent homology through both categorical and quiver theoretic viewpoints. While persistent homology has its roots in these topics, there ...

#### Effective numerical methods to model dynamic behavior of springs with torsion

(University of Missouri--Columbia, 2018)

The purpose of this thesis is to find effective algorithms to numerically solve certain systems of differential equations that arise from standard Newtonian mechanics. Numerical models of elastica has already been well ...