Abstract
We prove the existence of conformally paramaterized minimizers for parametric two-dimensional variational problems subject to partially free boundary conditions. We establish regularity of class \( H_{loc}^{2,2} \cap C^{1,\alpha } ,0 < \alpha < 1 \), up to the free boundary under the assumption that there exists a perfect dominance function in the sense of Morrey.
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References
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Dedicated to Professor O. A. Ladyzhenskaya in admiration
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Hildebrandt, S., von der Mosel, H. (2002). The Partially Free Boundary Problem for Parametric Double Integrals. In: Birman, M.S., Hildebrandt, S., Solonnikov, V.A., Uraltseva, N.N. (eds) Nonlinear Problems in Mathematical Physics and Related Topics I. International Mathematical Series, vol 1. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-0777-2_9
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DOI: https://doi.org/10.1007/978-1-4615-0777-2_9
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