Preprint 30/2002

The Douglas problem for parametric double integrals

Matthias Kurzke and Heiko von der Mosel

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Submission date: 22. Mar. 2002
Pages: 41
published in: Manuscripta mathematica, 110 (2003) 1, p. 93-114 
DOI number (of the published article): 10.1007/s00229-002-0325-5
MSC-Numbers: 49J45, 49Q10, 53A07, 53A10
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Let formula10 be a parametric variational double integral and formula12 be a system of distinct Jordan curves. We prove the existence of multiply connected, conformally parametrized minimizers of formula10 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 formula10-mimimizers, and we discuss regularity results up to the boundary which follow from corresponding results for the Plateau problem.

03.07.2017, 01:40