Variational integrals with a wide range of anisotropy
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- by M. Bildhauer, M. Fuchs and X. Zhong
- St. Petersburg Math. J. 18 (2007), 717-736
- DOI: https://doi.org/10.1090/S1061-0022-07-00970-3
- Published electronically: August 9, 2007
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Abstract:
Anisotropic variational integrals of $(p,q)$-growth are considered. For the scalar case, the interior $C^{1,\alpha }$-regularity of bounded local minimizers is proved under the assumption that $q\leq 2p$, and a famous counterexample of Giaquinta is discussed. In the vector case, some higher integrability result for the gradient is obtained.References
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Bibliographic Information
- M. Bildhauer
- Affiliation: Department of Mathematics, Saarland University, P.O. Box 15 11 50, D-66041 Saarbrücken, Germany
- Email: bibi@math.uni-sb.de
- M. Fuchs
- Affiliation: Department of Mathematics, Saarland University, P.O. Box 15 11 50, D-66041 Saarbrücken, Germany
- Email: fuchs@math.uni-sb.de
- X. Zhong
- Affiliation: Department of Mathematics and Statistics, University of Jyväskylä, P.O. Box 35, Finland
- Email: zhong@maths.jyu.fi
- Received by editor(s): April 22, 2006
- Published electronically: August 9, 2007
- © Copyright 2007 American Mathematical Society
- Journal: St. Petersburg Math. J. 18 (2007), 717-736
- MSC (2000): Primary 35J20; Secondary 35A15, 49Q20
- DOI: https://doi.org/10.1090/S1061-0022-07-00970-3
- MathSciNet review: 2301040