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On surfaces of prescribed weighted mean curvature

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Abstract

Utilising a weight matrix we study surfaces of prescribed weighted mean curvature which yield a natural generalisation to critical points of anisotropic surface energies. We first derive a differential equation for the normal of immersions with prescribed weighted mean curvature, generalising a result of Clarenz and von der Mosel. Next we study graphs of prescribed weighted mean curvature, for which a quasilinear elliptic equation is proved. Using this equation, we can show height and boundary gradient estimates. Finally, we solve the Dirichlet problem for graphs of prescribed weighted mean curvature.

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Authors and Affiliations

  1. Fakultät für Mathematik und Wirtschaftswissenschaften, Universität Ulm, Institut für Analysis, Helmholtzstr. 18, 89069, Ulm, Germany

    Matthias Bergner & Jens Dittrich

Authors
  1. Matthias Bergner
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  2. Jens Dittrich
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Correspondence to Matthias Bergner.

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Bergner, M., Dittrich, J. On surfaces of prescribed weighted mean curvature. Calc. Var. 33, 169–185 (2008). https://doi.org/10.1007/s00526-008-0161-x

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  • DOI: https://doi.org/10.1007/s00526-008-0161-x

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