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Geometric Analysis and Nonlinear Partial Differential Equations pp 265–296Cite as

Optimal Regularity Results via A-Harmonic Approximation

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Summary

We discuss a new approach to regularity theory for almost minimizers of variational integrals in geometric measure theory or in the classical calculus of variations. This method is direct, exhibiting the dependence of the regularity estimates on the structural data of the variational integrand in explicit form; it requires only weak growth and smoothness assumptions on the integrand; it allows a unified treatment of interior and boundary regularity; and it leads to new regularity results which give the best possible modulus of continuity for the derivative of the almost minimizer in a variety of situations.

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Authors and Affiliations

  1. Mathematisches Institut, der Universität Erlangen-Nürnberg, Bismarckstr. 1 1/2, D-91054, Erlangen, Germany

    Frank Duzaar & Joseph F. Grotowski

  2. Mathematisches Institut, der Heinrich-Heine-Universität Düsseldorf Universitätsstraße 1, D-40225, Düsseldorf, Germany

    Klaus Steffen

Authors
  1. Frank Duzaar
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  2. Joseph F. Grotowski
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  3. Klaus Steffen
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Editors and Affiliations

  1. Department of Mathematics, University of Bonn, Beringstraße 1, 53115, Bonn, Germany

    Stefan Hildebrandt  & Hermann Karcher  & 

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Duzaar, F., Grotowski, J.F., Steffen, K. (2003). Optimal Regularity Results via A-Harmonic Approximation. In: Hildebrandt, S., Karcher, H. (eds) Geometric Analysis and Nonlinear Partial Differential Equations. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55627-2_16

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  • DOI: https://doi.org/10.1007/978-3-642-55627-2_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44051-2

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