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Optimal Regularity Results via A-Harmonic Approximation

In: Geometric Analysis and Nonlinear Partial Differential Equations

Author

Listed:
  • Frank Duzaar

    (der Universität Erlangen-Nürnberg, Mathematisches Institut)

  • Joseph F. Grotowski

    (der Universität Erlangen-Nürnberg, Mathematisches Institut)

  • Klaus Steffen

    (der Heinrich-Heine-Universität Düsseldorf Universitätsstraße 1, Mathematisches Institut)

Abstract

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.

Suggested Citation

  • Frank Duzaar & Joseph F. Grotowski & Klaus Steffen, 2003. "Optimal Regularity Results via A-Harmonic Approximation," Springer Books, in: Stefan Hildebrandt & Hermann Karcher (ed.), Geometric Analysis and Nonlinear Partial Differential Equations, pages 265-296, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-55627-2_16
    DOI: 10.1007/978-3-642-55627-2_16
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