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Эта публикация цитируется в 228 научных статьях (всего в 228 статьях)
Статьи
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
Аннотация:
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.
Поступила в редакцию: 10.10.2014
Образец цитирования:
P. Baroni, M. Colombo, G. Mingione, “Nonautonomous functionals, borderline cases and related function classes”, Алгебра и анализ, 27:3 (2015), 6–50; St. Petersburg Math. J., 27:3 (2016), 347–379
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/aa1433 https://www.mathnet.ru/rus/aa/v27/i3/p6
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