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Topics in non-locally convex functional analysis and geometrical analysis with applications to boundary value problems
(University of Missouri--Columbia, 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 2-13, deals with issues pertaining to non-locally functional analysis. ...
Topics in harmonic analysis and partial differential equations: extension theorems and geometric maximum principles
(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 ...
Quasi-metric geometry
(University of Missouri--Columbia, 2014)
two objects is one of the most fundamental and ubiquitous in many branches of mathematics. A quasi-metric is a generalization of the familiar notion of metric. This dissertation examines what happens in this new setting of quasi-metrics. In particular...
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 ...
Surface to surface changes of variables and applications
(University of Missouri--Columbia, 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 ...
Sharp estimates of the transmission boundary value problem for dirac operators on non-smooth domains
(University of Missouri--Columbia, 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 ...
Topics in geometric analysis with applications to partial differential equations
(University of Missouri--Columbia, 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 the geometry is variable...
Boundary value problems for the Stokes system in arbitrary Lipschitz domains
(University of Missouri--Columbia, 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 Lp-data and nontangential maximal function estimates, (ii) the Neumann problem with Lp-data and ...
The poisson problem on Lipschitz domains
(University of Missouri--Columbia, 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 well-posed on the scales of Besov and Triebel-Lizorkin spaces ...
Quasi-metric geometry : smoothness and convergence results
(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 ...
Parabolic layer potentials and initial boundary value problems in Lipschitz cylinders with data in Besov spaces
(University of Missouri--Columbia, 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 ...