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St. Petersburg Mathematical Journal
St. Petersburg Mathematical Journal
ISSN 1547-7371(online) ISSN 1061-0022(print)

 

Variational integrals with a wide range of anisotropy


Authors: M. Bildhauer, M. Fuchs and X. Zhong
Original publication: Algebra i Analiz, tom 18 (2006), nomer 5.
Journal: St. Petersburg Math. J. 18 (2007), 717-736
MSC (2000): Primary 35J20; Secondary 35A15, 49Q20
Published electronically: August 9, 2007
MathSciNet review: 2301040
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Abstract | References | Similar Articles | Additional Information

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.


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Additional 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

DOI: http://dx.doi.org/10.1090/S1061-0022-07-00970-3
PII: S 1061-0022(07)00970-3
Keywords: Anisotropic problems, regularity of minimizers
Received by editor(s): April 22, 2006
Published electronically: August 9, 2007
Article copyright: © Copyright 2007 American Mathematical Society