• Absolute continuity of parabolic measure and the initial-dirichlet problem 

    Genschaw, Alyssa (University of Missouri--Columbia, 2019)
    This thesis is devoted to the study of parabolic measure corresponding to a divergence form parabolic operator. We first extend to the parabolic setting a number of basic results that are well known in the elliptic case. ...
  • 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 ...
  • Parabolic quantitative rectifiability 

    Hoffman, John L (University of Missouri--Columbia, 2023)
    The purpose of this thesis is to develop a parabolic analog of uniform rectifiability. First, we provide a very general result concerning corona decompositions and the big pieces functor. This result is stated in a very ...