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Now showing items 1-7 of 7

#### 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 ...

#### 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 ...

#### 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 ...

#### 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 ...

#### 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 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 ...

#### 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 ...