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Algebra i Analiz, 2009, Volume 21, Issue 5, Pages 203–221 (Mi aa1159)  
This article is cited in 4 scientific papers (total in 4 papers)

Research Papers

Regularity results for local minimizers of energies with general densities having superquadratic growth

M. Fuchs

Universität des Saarlandes, Fachbereich 6.1 Mathematik, Saarbrücken, Germany
Full-text PDF (262 kB) Citations (4)
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Abstract: Variational integrals whose energy densities are represented by NN-functions hh of at least quadratic growth are considered. Under rather general conditions on hh, almost everywhere regularity of vector-valued local minimizers is established, and it is possible to include the case of higher order variational problems without essential changes in the arguments.
Keywords: vector-valued problems, local minimizers, nonstandard growth, partial regularity.
Received: 08.08.2008
English version:
St. Petersburg Mathematical Journal, 2010, Volume 21, Issue 5, Pages 825–838
DOI: https://doi.org/10.1090/S1061-0022-2010-01120-8
Bibliographic databases:
Document Type: Article
MSC: 49N60
Language: English
Citation: M. Fuchs, “Regularity results for local minimizers of energies with general densities having superquadratic growth”, Algebra i Analiz, 21:5 (2009), 203–221; St. Petersburg Math. J., 21:5 (2010), 825–838
Citation in format AMSBIB
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Linking options:
  • https://www.mathnet.ru/eng/aa1159
  • https://www.mathnet.ru/eng/aa/v21/i5/p203
    • This publication is cited in the following 4 articles:
    1. Breit D., “Analysis of generalized Navier–Stokes equations for stationary shear thickening flows”, Nonlinear Anal., 75:14 (2012), 5549–5560  crossref  mathscinet  zmath  isi  scopus
    2. Breit D., Schirra O., “Korn-type inequalities in Orlicz-Sobolev spaces involving the trace-free part of the symmetric gradient and applications to regularity theory”, Z. Anal. Anwend., 31:3 (2012), 335–356  crossref  mathscinet  zmath  isi  elib  scopus
    3. Breit D., “Splitting-type variational problems with $x$-dependent exponents”, Ann. Acad. Sci. Fenn. Math., 36:1 (2011), 279–289  crossref  mathscinet  zmath  isi  scopus
    4. Breit D., Stroffolini B., Verde A., “A general regularity theorem for functionals with $\varphi$-growth”, J. Math. Anal. Appl., 383:1 (2011), 226–233  crossref  mathscinet  zmath  isi  elib  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Алгебра и анализ St. Petersburg Mathematical Journal
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