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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}
Linking options:
  • https://www.mathnet.ru/eng/aa88
  • https://www.mathnet.ru/eng/aa/v18/i5/p46
    • This publication is cited in the following 5 articles:
    1. Brasco L., Leone Ch., Pisante G., Verde A., “Sobolev and Lipschitz regularity for local minimizers of widely degenerate anisotropic functionals”, Nonlinear Anal.-Theory Methods Appl., 153:SI (2017), 169–199  crossref  mathscinet  zmath  isi  scopus
    2. Bousquet P., Brasco L., Julin V., “Lipschitz Regularity For Local Minimizers of Some Widely Degenerate Problems”, Ann. Scuola Norm. Super. Pisa-Cl. Sci., 16:4 (2016), 1235–1274  mathscinet  zmath  isi
    3. Brasco L., Carlier G., “On Certain Anisotropic Elliptic Equations Arising in Congested Optimal Transport: Local Gradient Bounds”, Adv. Calc. Var., 7:3 (2014), 379–407  crossref  mathscinet  zmath  isi  scopus
    4. Bildhauer M., Fuchs M., “Differentiability and higher integrability results for local minimizers of splitting-type variational integrals in 2D with applications to nonlinear Hencky-materials”, Calc. Var. Partial Differential Equations, 37:1-2 (2010), 167–186  crossref  mathscinet  zmath  isi  scopus
    5. Bildhauer M., Fuchs M., Zhong Xiao, “A regularity theory for scalar local minimizers of splitting-type variational integrals”, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), 6:3 (2007), 385–404  mathscinet  zmath  isi
    Citing articles in Google Scholar: Russian citations, English citations
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    		Алгебра и анализ St. Petersburg Mathematical Journal
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    References:56
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