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The Douglas problem for parametric double integrals

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Abstract.

 Let be a parametric variational double integral and γ ⊂ ℝn 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.

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Received: 19 April 2002

Mathematics Subject Classification (2000): 49J45, 49Q10, 53A07, 53A10

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Kurzke, M., von der Mosel, H. The Douglas problem for parametric double integrals. manuscripta math. 110, 93–114 (2003). https://doi.org/10.1007/s00229-002-0325-5

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  • DOI: https://doi.org/10.1007/s00229-002-0325-5

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