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Elliptic Variational Problems with Nonstandard Growth

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Nonlinear Problems in Mathematical Physics and Related Topics I

Part of the book series: International Mathematical Series ((IMAT,volume 1))

Abstract

For a bounded Lipschitz domain a minimization problem is considered over functions of the Orlicz-Sobolev space generated by an N-function A (with Δ2-property) that have prescribed trace u 0. Regularity results are established. In the vector case N > 1, partial C 1,α-regularity is proved without any additional structural conditions. The results are easily extended to the case of locally minimizing mappings. In the scalar case, the results obtained cover the case of (double) obstacles. Under an additional assumption, the regularity results can be improved (cf. Theorem 3 below which admits the anisotropic two-dimensional vector case).

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Authors
  1. Michael Bildhauer
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  2. Martin Fuchs
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Editor information

Editors and Affiliations

  1. St. Petersburg University, St. Petersburg, Russia

    Michael Sh. Birman  & Nina N. Uraltseva  & 

  2. University of Bonn, Bonn, Germany

    Stefan Hildebrandt

  3. Steklov Institute of Mathematics RAS, St. Petersburg, Russia

    Vsevolod A. Solonnikov

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Dedicated to O. A. Ladyzhenskaya on her birthday

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Bildhauer, M., Fuchs, M. (2002). Elliptic Variational Problems with Nonstandard Growth. 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_4

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  • DOI: https://doi.org/10.1007/978-1-4615-0777-2_4

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-5234-1

  • Online ISBN: 978-1-4615-0777-2

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