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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.

Received:
Mar 22, 2002
Published:
Mar 22, 2002
MSC Codes:
49J45, 49Q10, 53A07, 53A10

Related publications

inJournal
2003 Repository Open Access
Matthias Kurzke and Heiko von der Mosel

The Douglas problem for parametric double integrals

In: Manuscripta mathematica, 110 (2003) 1, pp. 93-114