• Geometric combinatorics in discrete settings 

    Covert, David (University of Missouri--Columbia, 2011)
    This thesis is a compilation of work in which the author studies geometric configurations in finite fields and the integers modulo q. The results of this dissertation are threefold. First, we prove a finite field analog ...
  • Nonlinear equations with natural growth terms 

    Jaye, Benjamin James (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 ...
  • Quasi-metric geometry: smoothness and convergence results 

    Brigham, Dan, 1987- (University of Missouri--Columbia, 2011)
    This thesis has two distinct yet related parts, the first pertaining to geometry on quasi-metric spaces with emphasis on the Hausdorff outer-measure, the natural extension of the Gromov-Pompeiu-Hausdorff distance to ...
  • Topics in harmonic analysis and partial differential equations: extension theorems and geometric maximum principles 

    Alvarado, Ryan (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 ...