Browsing Department of Mathematics (MU) by Thesis Advisor "Mitrea, Marius"
Now showing items 114 of 14

Boundary value problems for the Stokes system in arbitrary Lipschitz domains
(University of MissouriColumbia, 2008)The goal of this work is to treat the main boundary value problems for the Stokes system, i.e., (i) the Dirichlet problem with Lpdata and nontangential maximal function estimates, (ii) the Neumann problem with Lpdata and ... 
CalderonZygmund theory for singular integral operators associated with secondorder elliptic partial differential systems on rough subdomains of Riemannian manifolds
(University of MissouriColumbia, 2016)[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] This dissertation is a treatise on the theory of CalderonZygmund type singular integral operators capable of handling boundary layer potentials arising ... 
The implicit function theorem for Lipschitz functions and applications
(University of MissouriColumbia, 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 ... 
Parabolic layer potentials and initial boundary value problems in Lipschitz cylinders with data in Besov spaces
(University of MissouriColumbia, 2006)We adapt the method of boundary layer potentials to the Poisson problem for the heat operator [partial differential]t [delta] in a bounded Lipschitz cylinder, with Dirichlet and Neumann boundary conditions. When the lateral ... 
The poisson problem on Lipschitz domains
(University of MissouriColumbia, 2005)The aim of this work is to describe the sharp ranges of indices, for which the Poisson problem for Laplacian with Dirichlet or Neumann boundary conditions is wellposed on the scales of Besov and TriebelLizorkin spaces ... 
Quasimetric geometry
(University of MissouriColumbia, 2014)[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] Every time one sees xy, one is looking at a specific metric acting on x and y, whatever they may happen to be, usually numbers or vectors. The notion ... 
Quasimetric geometry: smoothness and convergence results
(University of MissouriColumbia, 2011)This thesis has two distinct yet related parts, the first pertaining to geometry on quasimetric spaces with emphasis on the Hausdorff outermeasure, the natural extension of the GromovPompeiuHausdorff distance to ... 
Sharp estimates of the transmission boundary value problem for dirac operators on nonsmooth domains
(University of MissouriColumbia, 2006)This thesis derives the sharp estimates for the transmission boundary value problems (TBVP) for Dirac operators in Lipschitz domains in the three dimensional setting. Most of the transmission problems considered in the ... 
Surface to surface changes of variables and applications
(University of MissouriColumbia, 2008)The present thesis addresses a number of basic problems in relation to integration over surfaces in the Euclidean space, such as how the surface measure and unit normal changes under a smooth diffeomorphism how the integration ... 
Topics in geometric analysis and harmonic analysis on spaces of homogeneous type
(University of MissouriColumbia, 2015)[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] The present dissertation consists of three main parts. One theme underscoring the work carried out in this dissertation concerns the relationship between ... 
Topics in geometric analysis with applications to partial differential equations
(University of MissouriColumbia, 2009)The main aim of the current thesis is to investigate the mathematical tools and methods used to study problems which bridge between analysis and geometry. Such an undertaking is particularly useful in situations in which ... 
Topics in harmonic analysis and partial differential equations: extension theorems and geometric maximum principles
(University of MissouriColumbia, 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 quasimetric space which satisfies a Höldertype condition may be extended ... 
Topics in nonlocally convex functional analysis and geometrical analysis with applications to boundary value problems
(University of MissouriColumbia, 2012)[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] This dissertation is comprised of two parts. The first part, consisting of chapters 213, deals with issues pertaining to nonlocally functional analysis. ... 
Trace/extension operators in rough domains and applications to partial differential equations
(University of MissouriColumbia, 2015)[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] Trace and extension theory lay the foundation for solving a plethora of boundary value problems. In developing this theory, one typically needs ...