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Algebra i Analiz, 2015, Volume 27, Issue 3, Pages 6–50 (Mi aa1433)  
This article is cited in 232 scientific papers (total in 232 papers)

Research Papers

Nonautonomous functionals, borderline cases and related function classes

P. Baronia, M. Colombob, G. Mingionec

a Department of Mathematics, Uppsala University, Lägerhyddsvägen 1, S-75106 Uppsala, Sweden
b Scuola Normale Superiore di Pisa, p.za dei Cavalieri 7, I-56126 Pisa, Italy
c Dipartimento di Matematica e Informatica, Università di Parma, Parco Area delle Scienze 53/a, Campus,,43100 Parma, Italy
Full-text PDF (444 kB) Citations (232)
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Abstract: The class of nonautonomous functionals under study is characterized by the fact that the energy density changes its ellipticity and growth properties according to the point; some regularity results are proved for related minimisers. These results are the borderline counterpart of analogous ones previously derived for nonautonomous functionals with $(p,q)$-growth. Also, similar functionals related to Musielak–Orlicz spaces are discussed, in which basic properties like the density of smooth functions, the boundedness of maximal and integral operators, and the validity of Sobolev type inequalities are related naturally to the assumptions needed to prove the regularity of minima.
Received: 10.10.2014
English version:
St. Petersburg Mathematical Journal, 2016, Volume 27, Issue 3, Pages 347–379
DOI: https://doi.org/10.1090/spmj/1392
Bibliographic databases:
Document Type: Article
Language: English
Citation: P. Baroni, M. Colombo, G. Mingione, “Nonautonomous functionals, borderline cases and related function classes”, Algebra i Analiz, 27:3 (2015), 6–50; St. Petersburg Math. J., 27:3 (2016), 347–379
Citation in format AMSBIB
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    • This publication is cited in the following 232 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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