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MiS Preprint
30/2002
The Douglas problem for parametric double integrals
Matthias Kurzke and Heiko von der Mosel
Abstract
Let $\mathcal{F}$ be a parametric variational double integral and $\Gamma\subset R^n$ be a system of distinct Jordan curves. We prove the existence of multiply connected, conformally parametrized minimizers of $\mathcal{F}$ by solving the Douglas problem for parametric functionals on multiply connected schlicht domains. As a by-product we obtain a simple isoperimetric inequality for multiply connected $\mathcal{F}$-mimimizers, and we discuss regularity results up to the boundary which follow from corresponding results for the Plateau problem.
