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Publications in Scientific Journals:

D. Praetorius:
"Analysis of the Operator $\Laplace^{-1}\div$ Arising in Magnetic Models";
Zeitschrift für Analysis und ihre Anwendungen (ZAA), 23 (2004), 589 - 605.

English abstract:
In the context of micromagnetics the partial differential equation

$\div(-\nabla u+\m)=0\text{ in }\R^d$

has to be solved in the entire space for a given magnetization
$\m:\Omega\to\R^d$ and $\Omega\subseteq\R^d$. For an $L^p$ function
$\m$ we show that the solution might fail to be in the classical
Sobolev space $W^{1,p}(\R^d)$ but has to be in a Beppo-Levi class
$W_1^p(\R^d)$. We prove unique solvability in $W_1^p(\R^d)$ and
provide a direct ansatz to obtain $u$ via a non-local integral
operator $\LL_p$ related to the Newtonian potential. A possible
discretization to compute $\nabla(\LL_2\m)$ is mentioned and it is
shown how recently established matrix compression techniques using
hierarchical matrices can be applied to the full matrix obtained from
the discrete operator.

Online library catalogue of the TU Vienna:
Electronic version of the publication:

Created from the Publication Database of the Vienna University of Technology.