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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Abstract:
Let be a parametric variational double integral and be a system of distinct Jordan curves. We prove the existence of multiply connected, conformally parametrized minimizers of 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 -mimimizers, and we discuss regularity results up to the boundary which follow from corresponding results for the Plateau problem.