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- Title
The Douglas problem for parametric double integrals.
- Authors
Kurzke, Matthias; von der Mosel, Heiko
- Abstract
Let be a parametric variational double integral and γ ⊂ ℝ n be a system of several distinct Jordan curves. We prove the existence of multiply connected, conformally parametrized minimizers of spanned in γ 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 -minimizers, and we discuss regularity results up to the boundary which follow from corresponding results for the Plateau problem.
- Publication
Manuscripta Mathematica, 2003, Vol 110, Issue 1, p93
- ISSN
0025-2611
- Publication type
Article
- DOI
10.1007/s00229-002-0325-5