• Adams inequalities with exact growth condition : on Rn and the Heisenberg group 

    Qin, Liuyu (University of Missouri--Columbia, 2020)
    In this thesis we prove sharp Adams inequality with exact growth condition for the Riesz potential as well as the more general strictly Riesz-like potentials on R[superscript n]. Then we derive the Moser-Trudinger type ...
  • Critical perturbations of elliptic operators by lower order terms 

    Luna-Garcia, Jose Luis (University of Missouri--Columbia, 2021)
    In this work we study issues of existence and uniqueness of solutions of certain boundary value problems for elliptic equations in the upper half-space. More specifically we treat the Dirichlet, Neumann, and Regularity ...
  • Entropy minimization, convergence, and Gibbs ensembles (local and global) 

    Hughes, Alexander M. (University of Missouri--Columbia, 2021)
    We approach the subject of Statistical Mechanics from two different perspectives. In Part I we adopt the approach of Lanford and Martin-Lof. We examine the minimization of information entropy for measures on the phase space ...
  • Linear and multilinear spherical maximal functions 

    Ntosidis, Georgios (University of Missouri--Columbia, 2020)
    In dimensions n [greater than or equal to] 2 we obtain Lp1(Rn) x ... x Lpm(Rn) to Lp(Rn) boundedness for the multilinear spherical maximal function in the largest possible open set of indices and we provide counterexamples ...
  • M-adic perturbations in Noetherian local rings 

    Cox-Steib, Nicholas O. (University of Missouri--Columbia, 2021)
    The purpose of this thesis is to develop methods for the study m-adic stability in an arbitrary Noetherian local ring. A key role is played by the Artin-Rees lemma. Using these techniques we establish new results about the ...
  • Mathematical and computational modeling of fluid flow with applications in ophthalmology and geoscience 

    Abdelhafid, Farah (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 ...
  • Stochastic forms of functional isoperimetric inequalities 

    Rebollo Bueno, Jesus (University of Missouri--Columbia, 2021)
    The Brunn-Minkowski and Prekopa-Leindler inequalities admit a variety of proofs that are inspired by convexity. Nevertheless, the former holds for compact sets and the latter for integrable functions, so it seems that ...
  • Structural features of persistent homology and their algorithmic transformations 

    Pavlichenko, Andrei (University of Missouri--Columbia, 2021)
    We re-examine the theory and orthodox methods that underlie the study of persistent homology, particularly in its calculation of homological cycle representatives that are associated to persistence diagrams. A common ...
  • Volumes of line bundles on schemes 

    Nunez, Roberto (University of Missouri--Columbia, 2021)
    The volume of a line bundle is an invariant defined in terms of a limit superior. It is a fundamental question whether this limit superior is a limit. It has been shown that this is always the case on generically reduced ...