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Journal of Mathematical Sciences

, Volume 175, Issue 3, pp 375–389 | Cite as

Two-dimensional variational problems with a wide range of anisotropy

  • M. Fuchs
Article
  • 16 Downloads
We consider local minimizers \( u:{\mathbb{R}^2} \supset \Omega \to {\mathbb{R}^M} \) of the variational integral
$$ \int\limits_\Omega {H\left( {\nabla u} \right)dx} $$
with density H growing at least quadratically and allowing a very large scale of anisotropy. We discuss higher integrability properties of ∇u and the differentiability of u in the classical sense. A Liouville type theorem is also established. Bibliography: 25 titles.

Keywords

High Integrability Partial Regularity Sobolev Embedding Theorem Liouville Type Theorem Nonstandard Growth 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, Inc. 2011

Authors and Affiliations

  1. 1.Universität des Saarlandes, Fachbereich 6.1 MathematikSaarbrückenGermany

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