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Algebra i Analiz, 2006, Volume 18, Issue 5, Pages 46–71 (Mi aa88)  
This article is cited in 5 scientific papers (total in 5 papers)

Research Papers

Variational integrals with a wide range of anisotropy

M. Bildhauera, M. Fuchsa, X. Zhongbc

a Saarland University, Department of Mathematics, Saarbrücken, Germany
b Department of Mathematics and Statistics, University of Jyväskylä, Finland
c Wuhan Institute of Physics and Mathematics, The Chinese Academy of Sciences
Full-text PDF (265 kB) Citations (5)
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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 $q\le 2p$, and a famous counterexample of Giaquinta is discussed. In the vector case, some higher integrability result for the gradient is obtained.
Keywords: anisotropic problems, regularity of minimizers.
Received: 22.04.2006
English version:
St. Petersburg Mathematical Journal, 2007, Volume 18, Issue 5, Pages 717–736
DOI: https://doi.org/10.1090/S1061-0022-07-00970-3
Bibliographic databases:
Document Type: Article
MSC: Primary 35J20; Secondary 35A15, 49Q20
Language: English
Citation: M. Bildhauer, M. Fuchs, X. Zhong, “Variational integrals with a wide range of anisotropy”, Algebra i Analiz, 18:5 (2006), 46–71; St. Petersburg Math. J., 18:5 (2007), 717–736
Citation in format AMSBIB
\Bibitem{BilFucZho06}
\by M.~Bildhauer, M.~Fuchs, X.~Zhong
\paper Variational integrals with a~wide range of anisotropy
\jour Algebra i Analiz
\yr 2006
\vol 18
\issue 5
\pages 46--71
\mathnet{http://mi.mathnet.ru/aa88}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2301040}
\zmath{https://zbmath.org/?q=an:05232563}
\transl
\jour St. Petersburg Math. J.
\yr 2007
\vol 18
\issue 5
\pages 717--736
\crossref{https://doi.org/10.1090/S1061-0022-07-00970-3}
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Алгебра и анализ St. Petersburg Mathematical Journal
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