Delve into the future of research at MiS with our preprint repository. Our scientists are making groundbreaking discoveries and sharing their latest findings before they are published. Explore repository to stay up-to-date on the newest developments and breakthroughs.
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.