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Алгебра и анализ, 2015, том 27, выпуск 3, страницы 6–50 (Mi aa1433)  

Эта публикация цитируется в 235 научных статьях (всего в 235 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
Список литературы:
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
Англоязычная версия:
St. Petersburg Mathematical Journal, 2016, Volume 27, Issue 3, Pages 347–379
DOI: https://doi.org/10.1090/spmj/1392
Реферативные базы данных:
Тип публикации: Статья
Язык публикации: английский
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
Цитирование в формате AMSBIB
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Образцы ссылок на эту страницу:
  • https://www.mathnet.ru/rus/aa1433
  • https://www.mathnet.ru/rus/aa/v27/i3/p6
  • Эта публикация цитируется в следующих 235 статьяx:
    1. Nour Eddine Alaa, Mostafa Bendahmane, Abderrahim Charkaoui, “Well-posedness results to parabolic problems involving (p(x),q(x))-growth structure with L1-data”, Journal of Mathematical Analysis and Applications, 543:2 (2025), 128934  crossref
    2. Ge Dong, Xiaochun Fang, “Existence and L-Estimates of the Solutions to a Class of Inclusion Problems”, Bull. Malays. Math. Sci. Soc., 48:1 (2025)  crossref
    3. Takao Ohno, Tetsu Shimomura, “Boundedness of maximal operators and Sobolev inequalities on Musielak-Orlicz spaces over unbounded metric measure spaces”, Bulletin des Sciences Mathématiques, 199 (2025), 103546  crossref
    4. Minh-Phuong Tran, Thanh-Nhan Nguyen, “Existence of weak solutions to borderline double-phase problems with logarithmic convection terms”, Journal of Mathematical Analysis and Applications, 546:1 (2025), 129185  crossref
    5. Ahmed El Ouardani, Ahmed Aberqi, Omar Benslimane, Mhamed El Massoudi, “Investigation into double-phase elliptic problems with boundary conditions, incorporating a logarithmic convection term”, J. Pseudo-Differ. Oper. Appl., 16:1 (2025)  crossref
    6. Haiyan Zhou, Xiaoqian Song, Songbai Wang, Jiang Zhou, “Hardy–Littlewood maximal operators and generalized Orlicz spaces on measure spaces”, Ann. Funct. Anal., 16:1 (2025)  crossref
    7. Ángel Crespo-Blanco, Patrick Winkert, “Nehari manifold approach for superlinear double phase problems with variable exponents”, Annali di Matematica, 203:2 (2024), 605  crossref
    8. Yongjian Liu, Yasi Lu, Calogero Vetro, “A new kind of double phase elliptic inclusions with logarithmic perturbation terms I: Existence and extremality results”, Communications in Nonlinear Science and Numerical Simulation, 129 (2024), 107683  crossref
    9. Hoang Hai Ha, Ky Ho, “Multiplicity results for double phase problems involving a new type of critical growth”, Journal of Mathematical Analysis and Applications, 530:1 (2024), 127659  crossref
    10. Igor Skrypnik, Yevgeniia Yevgenieva, “Harnack inequality for solutions of the p(x)-Laplace equation under the precise non-logarithmic Zhikov's conditions”, Calc. Var., 63:1 (2024)  crossref
    11. Nikolaos S. Papageorgiou, Francesca Vetro, Patrick Winkert, “Sequences of nodal solutions for critical double phase problems with variable exponents”, Z. Angew. Math. Phys., 75:3 (2024)  crossref
    12. D. E. Apushkinskaya, A. A. Arkhipova, A. I. Nazarov, V. G. Osmolovskii, N. N. Uraltseva, “A Survey of Results of St. Petersburg State University Research School on Nonlinear Partial Differential Equations. I”, Vestnik St.Petersb. Univ.Math., 57:1 (2024), 1  crossref
    13. Atsushi Tachikawa, “Partial regularity of minimizers for double phase functionals with variable exponents”, Nonlinear Differ. Equ. Appl., 31:2 (2024)  crossref
    14. Mariia Savchenko, Igor Skrypnik, Yevgeniia Yevgenieva, “On the weak Harnack inequality for unbounded non-negative super-solutions of degenerate double-phase parabolic equations”, Journal of Mathematical Analysis and Applications, 537:2 (2024), 128331  crossref
    15. Calogero Vetro, Shengda Zeng, “Regularity and Dirichlet Problem for Double-Phase Energy Functionals of Different Power Growth”, J Geom Anal, 34:4 (2024)  crossref
    16. Minh-Phuong Tran, Thanh-Nhan Nguyen, Le-Tuyet-Nhi Pham, “Gradient bounds for non-uniformly quasilinear elliptic two-sided obstacle problems with variable exponents”, Journal of Mathematical Analysis and Applications, 531:1 (2024), 127776  crossref
    17. Anna Kh. Balci, Mikhail Surnachev, “The Lavrentiev phenomenon in calculus of variations with differential forms”, Calc. Var., 63:3 (2024)  crossref
    18. Maria Alessandra Ragusa, Atsushi Tachikawa, “Regularity of minimizers for double phase functionals of borderline case with variable exponents”, Advances in Nonlinear Analysis, 13:1 (2024)  crossref
    19. Wulong Liu, Guowei Dai, Patrick Winkert, Shengda Zeng, “Multiple Positive Solutions for Quasilinear Elliptic Problems in Expanding Domains”, Appl Math Optim, 90:1 (2024)  crossref
    20. Ky Ho, Yun-Ho Kim, Chao Zhang, “Double phase anisotropic variational problems involving critical growth”, Advances in Nonlinear Analysis, 13:1 (2024)  crossref
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    Алгебра и анализ St. Petersburg Mathematical Journal
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