Analysis of the Operator Δ^-1div Arising in Magnetic Models

  • Dirk Praetorius

    Technische Universität Wien, Austria


In the context of micromagnetics the partial differential equation

has to be solved in the entire space for a given magnetization and . For an function we show that the solution might fail to be in the classical Sobolev space but has to be in a Beppo-Levi class . We prove unique solvability in and provide a direct ansatz to obtain via a non-local integral operator related to the Newtonian potential. A possible discretization to compute 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.

Cite this article

Dirk Praetorius, Analysis of the Operator Δ^-1div Arising in Magnetic Models. Z. Anal. Anwend. 23 (2004), no. 3, pp. 589–605

DOI 10.4171/ZAA/1212