Plateaus' problem for parametric double integrals: I. Existence and regularity in the interior
Stefan Hildebrandt and Heiko von der Mosel
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Submission date: 20. Nov. 2001
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We study Plateau's problem for two-dimensional parametric integrals
the Lagrangian F(x,z) of which is positive definite and at least semi-elliptic. It turns out that there always exists a conformally para-me-trized minimizer. Any such minimizer X is seen to be Hölder continuous in the parameter domain B and continuous up to its boundary. If F possesses a perfect dominance function G of class we can establish higher regularity of X in the interior. In fact, we prove for some Finally we discuss the existence of perfect dominance functions.