Optimal Regularity Results via A-Harmonic Approximation

Frank Duzaar (), Joseph F. Grotowski () and Klaus Steffen ()
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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

A chapter in Geometric Analysis and Nonlinear Partial Differential Equations, 2003, pp 265-296 from Springer

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.

Keywords: Regularity Result; Partial Regularity; Boundary Regularity; Geometric Measure Theory; Nonlinear Elliptic System (search for similar items in EconPapers)
Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-55627-2_16

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DOI: 10.1007/978-3-642-55627-2_16

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